In his U.N. speech, President Biden called for collective action on Ukraine and other major crises.

“They have put people on horseback to chase with whips in their hands, with stocks and chains,” Mr. Petro said. “They have built prisons. They have grown so much in their hatred of the foreigner, of the stranger, that the prisons have been placed in the sea, so that the men and women of the south do not set foot in the lands of white people, who still consider themselves the superior race.”

Mr. Petro is Colombia’s first leftist president, and has been far more critical of the United States than his predecessors. The speech came as Mr. Petro has struggled with a humanitarian crisis at home, as hundreds of thousands of people from all over the world have arrived in northern Colombia in the last two years, all of them set on crossing the Dari?n Gap, the treacherous jungle that is the only land route from South America to the United States.

Mr. Petro’s government signed an agreement in April with the United States in which both nations said they would seek to “end the illicit movement of people and goods through the Dari?n.”

But in a recent interview with The New York Times, Mr. Petro said it was not his goal to stop this flow, at least not with the police or military force. Instead, he said, the United States needed to focus on changing policies that he believed caused migration — including, he said, U.S. sanctions on Venezuela.

In his speech on Tuesday, Mr. Petro warned that if powerful nations did not address issues like climate change, migration would only grow. “The exodus of peoples to the north is a precise measurement of the scale of governments’ failure,” he said.

“Today there are tens of millions,” he went on. “In the year 2070 there will be three billion fleeing their beloved places, because they will be uninhabitable. In my homeland, the country of beauty, Colombia, the country of explosion of life, in 2070, only deserts will remain. The people will go north, no longer attracted by the sequins of wealth, but by something simpler and more vital: water.”

The United States and Ecuador are expected to submit a joint resolution to the U.N. Security Council next week officially proposing the Kenyan mission.

In his speech to the General Assembly Tuesday, President Biden urged the members to authorize the mission.

“The people of Haiti cannot wait much longer,” he said.

But the core purpose of the international security mission emerged as a key stumbling block after the Kenyans initially suggested that it be used to guard important government infrastructure, such as ports, in order to enable the flow of humanitarian assistance and commerce.

A senior State Department official who was not authorized to speak publicly about sensitive discussions said the Kenyans have also agreed to provide operational support in the Haitian National Police’s battle against gangs and also agreed to help strengthen the Haitian Police.

The Kenyan Foreign Ministry did not return repeated requests for comment.

The United States has said it will also provide support — but not soldiers. Instead, it is offering financing and in-kind support from the Department of Defense, which would include logistics, intelligence, surveillance and reconnaissance, the senior official said.

Haitians are sensitive to the idea of any kind of international security effort, particularly given the problems that arose with past United Nations peacekeeping forces. Poor sanitation at a U.N. compound brought cholera to Haiti, and human rights organizations denounced the number of children that U.N. soldiers fathered and abandoned.

This week’s talks include accountability measures, efforts to prevent and combat sexual exploitation and abuse, cholera and improved water standards and sanitation, the U.S. official said.

A spokesman for the Haitian delegation did not immediately respond to a request for comment Tuesday.

Climate change is causing rain in many places to fall in shorter but more intense bursts. Climate scientists have been projecting stronger storms for “a long time now,” Dr. Otto said.

“It is a worldwide phenomenon,” said Kostas Lagouvardos, a meteorologist and research director at the National Observatory of Athens. “When it rains today, it rains a lot.”

The scientists are part of World Weather Attribution, a coalition of scientists that investigates the role of climate change in extreme weather events. The scientists use a peer-reviewed method to compare today’s climate, which has been warmed by the burning of fossil fuels, with a climate of the past.

This kind of rainfall is still extremely unusual in Libya, the scientists said, and even in today’s climate is only likely to occur once in every 300 to 600 years. (Each year, there is a less than 1 percent chance of similar storms happening). They also pointed out that the rain combined with the region’s built environment, leading to disastrous flooding that has killed and displaced thousands.

In contrast, the heavy but less extreme rainfall over the larger region encompassing Bulgaria, Greece and Turkey is now a relatively common weather phenomenon. Similar amounts of rain are likely to fall once every 10 years, or have a 10 percent chance of happening each year. A smaller area in central Greece received more extreme rain than the rest of the region, leading to at least 17 deaths.

A lot has changed since then. Here are some major events in the war:

September 2022

In a rapid offensive, Ukraine retook much of the northeastern Kharkiv region and seized the initiative in the war. Ukraine would recapture the eastern city of Lyman the next month.

October

In a blow to Moscow’s war effort, an explosion damaged the Kerch Strait Bridge linking occupied Crimea with the Russian mainland. Two days later, Russia launched a barrage of airstrikes against Ukraine, the start of a campaign against the country’s energy infrastructure.

Russia announced the annexation of four Ukrainian regions despite international condemnation and its loss of ground in some of those areas.

November

Russian forces withdrew from the city of Kherson to the eastern side of the Dnipro River after weeks of steady attacks from Ukraine, a significant victory for Kyiv.

December

With little territory changing hands on the battlefield, Ukraine carried out drone attacks on military bases hundreds of miles inside Russia.

January 2023

Ukrainian forces struck a building in Donetsk that was housing Russian troops. Moscow acknowledged the deaths of 89 soldiers in the attack; Ukraine said hundreds had been killed or wounded.

Moscow launched waves of missile and drone strikes aimed at crippling Ukraine’s energy grid during subfreezing winter weather, killing civilians. The campaign mostly failed because of Ukraine’s ability to quickly repair the damage.

March

The International Criminal Court accused President Vladimir V. Putin of Russia of war crimes and issued a warrant for his arrest.

The court cited Mr. Putin’s responsibility for the abduction and deportation of Ukrainian children, thousands of whom have been sent to Russia since the invasion. It also issued a warrant for Russia’s commissioner for children’s rights, Maria Lvova-Belova, the public face of the Kremlin-sponsored program that transfers children out of Ukraine.

Xi Jinping, China’s top leader, and Mr. Putin met face to face on March 20 in Moscow, where Mr. Xi hailed the two nations as “good neighbors and reliable partners.” China had been pushing a peace plan that many Western diplomats saw as tilting toward Russia.

April

Russia launched its first widespread aerial assault in months against civilian targets, killing at least 25 people, in a return to its tactic of bombarding cities far from the front line to demoralize Ukrainians.

A classified document leak traced to an American airman suggested that Ukrainian forces were in more dire straits than Kyiv’s government had acknowledged and in need of ammunition for its air defenses.

May

Ukrainian forces that had been holding out in a small section of the eastern city of Bakhmut were pushed out of the area after months of brutal fighting, giving Russia a costly victory. Wagner mercenaries had spearheaded the Russian assault, though they took heavy losses. The fighting continues just outside the city, however.

Drone attacks on the Kremlin marked the start of a new phase in the war. Over the next two months, Ukraine launched numerous drone attacks deep into Russian territory, a New York Times analysis found.

June

A major dam on the Dnipro River was destroyed by an explosion on June 6, flooding the war zone downstream, wreaking destruction on dozens of towns and causing environmental destruction.

A few days later, Ukraine’s forces, after months of anticipation, launched a counteroffensive aimed at driving a wedge between Russian forces in the south. The attack employed brigades trained by the West in complex warfare tactics and armed with billions of dollars of NATO armor and other sophisticated weaponry.

On June 24, the founder of the private Wagner mercenary force, Yevgeny V. Prigozhin, carried out a brief rebellion against the Kremlin after claiming the Russian Army had attacked his fighters. Though Mr. Prigozhin ended the mutiny after a day, he was later killed in a plane explosion that was widely seen by Western intelligence officials as a Kremlin-orchestrated assassination.

July

Russia pulled out of a wartime agreement brokered by the United Nations and Turkey that had allowed Ukraine to export grain through the Black Sea. Over the following weeks, Moscow launched numerous aerial assaults on Ukraine’s ports, further crippling its ability to ship grain.

August

Stian Jenssen, chief of staff of NATO’s secretary general, set off a storm of criticism in Ukraine and was forced to apologize after he raised the possibility of negotiations and Ukraine’s surrendering land as options for ending the war. “I think that a solution could be for Ukraine to give up territory and get NATO membership in return,” he said during a panel in Norway.

Though he added the standard line, “It must be up to Ukraine to decide when and on what terms they want to negotiate,” his comments underscored how talking openly about peace deals with Russia has become taboo among Ukraine’s allies.

Instead, Ukrainian forces initially made almost no progress. The pace of gains has increased in recent weeks, although Kyiv’s troops have yet to decisively penetrate the Russian defenses while also taking heavy casualties.

But war tends to be a grind. The types of routs that let Ukraine retake thousands of square miles in the northeast last year are rare. Fighting frequently involves chipping away at an enemy, like Ukraine’s retaking of a small but strategic village in the east on Sunday. Such advances try to build toward a big breakthrough, although one may never come.

That was true most famously during the trench warfare of World War I but also in World War II, the Korean War and the U.S. Civil War. “War is not always the spectacular triumph,” said George Barros, an analyst at the Institute for the Study of War. “It’s largely the really boring stuff that you don’t see — all the groundwork setting up the conditions for the triumphs.”

In other words: Ukraine and its allies, including the United States, may have set their expectations for the counteroffensive too high.

Ukraine’s leaders still hope to achieve a breakthrough that divides Russian troops in the east and south, but movements will become more difficult in the weeks ahead: By November, muddy season will have arrived.

The military’s initial plan was to use infantry, tanks and other armored vehicles supplied by the West to roll through Russian forces in Ukraine’s southeast, splitting off Russian troops in the occupied peninsula of Crimea from the eastern region of Donbas, hindering Moscow’s ability to reinforce or resupply its armies in either area.

But Ukrainian forces ran into staunch Russian defenses, particularly large minefields, and those early efforts proved costly, in both lives and equipment. So Ukraine’s military changed its approach, focusing more on wearing down the Russian forces with artillery and long-range missiles.

Last month, Kyiv’s troops finally made modest but meaningful gains, piercing Russia’s first line of defense in the southeast. Ukraine’s military in recent days says it has retaken two more villages in the east.

“Offenses are not linear affairs,” said Stacie Goddard, an international security expert at Wellesley College.

Ukraine’s military wants to widen the lanes its forces have opened through Russia’s first lines of defense, which could allow it to move many more forces through and try to carry out the original plan for a swift counteroffensive.

And if Russia has stationed its strongest forces on the front line, Ukraine could break through subsequent lines more easily. “A lot depends on how strong these remaining Russian defenses are,” my colleague Eric Schmitt, who covers national security, told me.

But the time to make a rapid advance could be dwindling. As rain arrives this fall, the terrain will get muddier and harder to traverse, likely preventing major battlefield gains.

In the meantime, Russian forces have stepped up attacks in the northeast. In doing so, Russia hopes to retake some of the territory it lost last year, and force Ukraine to divert its troops and resources to the northeast. If enough Ukrainian forces are kept from the southeastern front, the counteroffensive’s last big push could fail.

The Biden administration has sought to emphasize its commitment to addressing climate change, highlighting the president’s role in shepherding through the most ambitious climate law in recent years and making $370 billion in public funds available for the transition to renewable energy.

But at the same time, the administration has continued to issue permits for new oil and gas projects, infuriating many voters for whom climate change is a major issue, especially in the progressive flank of the Democratic Party.

The United States also remains a top producer and exporter of oil and gas.

“While we commend the Biden administration’s investments in the energy transition to renewables, it is crucial to recognize that true climate leadership starts by tackling what’s fueling the crisis: unhinged oil and gas expansion,” Ebony Twilley Martin, head of Greenpeace USA, said.

Last September, Mr. Zelensky delivered his address by video, remaining in Kyiv, the Ukrainian capital, where his presence had become a symbol of the government’s defiance. This year, he will attend the U.N. event in person as part of a flurry of diplomacy intended to press Ukraine’s cause.

Mr. Zelensky is expected to use his speech to again call for military and diplomatic support for Ukraine’s war effort, including modern battle tanks, rocket systems and air defenses.

After he landed in New York City on Monday, he visited Staten Island University Hospital, where Ukrainian soldiers are being treated for war injuries, photos on his channel on the Telegram messaging app showed.

One objective of Mr. Zelensky’s visit to the United States will most likely be to rebut calls by some conservatives in the United States for stricter limits to be placed on the amount of aid that Washington gives to Ukraine. At the same time, he must seek to drum up support for his country’s cause among nations that have avoided taking sides in the war, including South Africa, India and Brazil.

Mr. Zelensky visiting with wounded Ukrainian soldiers at Staten Island University Hospital in New York on Monday.Credit…Angela Weiss/Agence France-Presse — Getty Images

In one measure of the challenge Mr. Zelensky faces, his speech will come just weeks after the Group of 20 summit in New Delhi declined to condemn Russia for its invasion or its conduct in the 19 months since it launched its full-scale invasion. It merely lamented the “suffering” of the Ukrainian people.

Another issue likely to be a focus of Mr. Zelensky’s speech is grain, a major Ukrainian export. In July, Russia terminated a deal that allowed ships to carry grain from Ukrainian ports on the Black Sea, bypassing a Russian blockade, to world markets. The United Nations says that decision threatens millions of people in parts of Africa and the Middle East who face hunger.

After the address, Mr. Zelensky plans to travel to Washington to meet with congressional leaders and to visit the White House.

A year ago, Ukraine was pursuing an offensive that saw its forces retake a large part of the Kharkiv region in the northeast. In November it drove Russian soldiers from the city of Kherson and recaptured part of the southern region.

This time, the military context is also different. Russian forces took the eastern city of Bakhmut in May after months of brutal fighting. Ukraine, which launched a counteroffensive the following month, has faced stiff resistance from Russian forces and has yet to make a decisive breakthrough.

Mr. Zelensky has also said that Russia is hoping an opponent of military aid to Ukraine will win the next U.S. presidential election.

But Secretary of State Antony J. Blinken has pledged that the United States will continue to support Ukraine. And the Biden administration is working to shore up support in Congress for an additional $24 billion in military and humanitarian aid for Ukraine.

Michael Crowley and Karoun Demirjian contributed reporting.

“Russia believes that the world will grow weary and allow it to brutalize Ukraine without consequence,” Mr. Biden said as President Volodymyr Zelensky of Ukraine watched from the audience. “But I ask you this: If we abandon the core principles” of the United Nations Charter “to appease an aggressor, can any member state in this body feel confident that they are protected? If we allow Ukraine to be carved up, is the independence of any nation secure? I respectfully suggest the answer is no.”

“We have to stand up to this naked aggression today to deter other would-be aggressors tomorrow,” Mr. Biden continued. “That’s why the United States, together with our allies and partners around the world, will continue to stand with the brave people of Ukraine as they defend their sovereignty and territorial integrity — and their freedom.”

Mr. Zelensky offered his own stirring speech not long afterward, arguing to the assembled leaders and diplomats that President Vladimir V. Putin’s war against Ukraine was a war against all of their nations as well. He accused Moscow of weaponizing food, energy and even children with dire effects not just in his country but in far-flung corners of the world.

“The goal of the present war against Ukraine is to turn our land, our people, our lives, our resources into a weapon against you, against the international rules-based order,” said Mr. Zelensky, speaking in English and wearing one of his trademark olive green military-style shirts. “We have to stop it,” he added. “We must act united to defeat the aggressor.”

He dismissed efforts to broker a peace deal without Ukraine’s involvement, what he called “shady dealings behind the scenes.” Characterizing Russia as an unreliable partner, he cited the recent death of Yevgeny Prigozhin, the mercenary leader who had defied Mr. Putin. “Evil cannot be trusted,” Mr. Zelensky said. “Ask Prigozhin if one bets on Putin’s promises.”

Both Mr. Biden and Mr. Zelensky received strong applause from some of the delegations in the hall, but many others sat on their hands. Mr. Putin, the target of an arrest warrant for war crimes issued by the International Criminal Court, did not come to New York for the annual opening session, but his envoy sat in Russia’s seat during Mr. Zelensky’s speech taking notes or looking down at his telephone.

Mr. Zelensky was to address the U.N. Security Council on Wednesday with a plan to discourage war even after the fighting in his country eventually ends and then will head to Washington, where on Thursday he will meet with Mr. Biden at the White House, stop by the Pentagon and visit Capitol Hill to plead for continuing assistance. Unlike his first wartime trip to Washington last winter, he will not address a joint meeting of Congress and will find more resistance among some far-right Republicans in the House who are trying to block Mr. Biden’s request for $24 billion more aid.

Mr. Biden has continued to provide aid using previously approved funds, and Defense Secretary Lloyd J. Austin III announced on Tuesday that American M-1 tanks would be arriving in Ukraine soon. “That will add another formidable armor capability to join the weapons that are already on the battlefield,” he said in Germany after a meeting of about 50 countries supporting Ukraine. He added: “I salute Ukraine’s brave forces, and we’ve got their backs. Ukraine’s fight is one of the one of the great causes of our time.”

Mr. Biden’s speech came as other major leaders skipped the annual opening session of the General Assembly, including Mr. Putin and President Xi Jinping of China, effectively leaving the stage to the American president. He used the opportunity to reach out to the so-called global south — the traditionally unaligned developing nations that his advisers call the “swing states” of the foreign policy world — to enlist them to the American view of the threats that Russia and China pose to the international system.

While he took an unrelenting stance against Russia’s brutal war and warned against appeasing Moscow, he drew a more measured line on China, repeating his commitment to “push back on intimidation” by Beijing while seeking ways to work together and denying that he was trying to contain the Asian giant. “We seek to responsibly manage the competition between our countries so it does not tip into conflict,” he said.

Mr. Biden mentioned a litany of other major issues confronting the world today, like fentanyl abuse, artificial intelligence, terrorism, human rights, women’s rights, L.G.B.T. rights and arms control, without breaking much new ground on any of them. He stressed the dangers of climate change as he urged more action to combat it, citing heat waves, wildfires, drought and the flooding in Libya.

“Together, these snapshots tell an urgent story of what awaits us if we fail to reduce our dependence on fossil fuels and begin to climate-proof the world,” he said. Under his administration, he said, “the United States has treated this crisis as the existential threat from the moment we took office, not only for us, but for all of humanity.”

Mr. Biden will be using his time at the United Nations this week to meet with other world leaders. He met Tuesday afternoon with the leaders of the five Central Asian republics that used to be part of the Soviet Union — Uzbekistan, Kazakhstan, Kyrgyzstan, Tajikistan and Turkmenistan — the first time a president has sat down collectively with counterparts with those countries.

The “Stans,” as they are often called by diplomats, have been a key area of competition between Russia and China in the years since they gained their independence from the Soviet collapse, but the United States has sought influence there as well, particularly during its ill-fated war in Afghanistan. Mr. Biden’s meeting with their leaders is in keeping with his strategy of bolstering relations with nations in China’s neighborhood to counter assertive actions by Beijing.

On Tuesday evening, Mr. Biden and Jill Biden were to host a reception for other world leaders at the Metropolitan Museum of Art. On Wednesday, he was scheduled to sit down separately with Prime Minister Benjamin Netanyahu of Israel and President Luiz In?cio Lula da Silva of Brazil.

His meeting with Mr. Netanyahu will be their first in the United States since Mr. Biden became president, a much-delayed get-together that, tellingly, will not take place at the White House amid tension over Mr. Biden’s outreach to Iran and the Israeli leader’s efforts to diminish the power of courts in his country. In his speech on Tuesday, Mr. Biden touted his efforts to open diplomatic relations between Israel and Saudi Arabia while emphasizing his support for a two-state solution to Israel’s conflict with Palestinians.

While Russia and Ukraine were only a portion of his address, far less so than last year, they represented the core tension in the room as one of the United Nations’ founding members and permanent Security Council members was excoriated from the famed emerald green rostrum. Mr. Biden complained that Mr. Putin had been “shredding longstanding arms control agreements,” while Mr. Zelensky noted that his country had given up its nuclear weapons in exchange for a promise by Russia to respect its independence, a promise now violently broken.

Mr. Zelensky said that tens of thousands of Ukrainian children had been taken from occupied territory, sent to Russia and, he added, turned against their home country and relatives. “This is clearly a genocide,” Mr. Zelensky said. “When hatred is weaponized against one nation, it never stops there.”

“Each decade, Russia starts a new war,” he added, noting Moscow’s invasions and military interventions in Moldova, Georgia and Syria as well as its pressure on Belarus, Kazakhstan and the Baltic republics.

“War crimes must be punished, deported people must come home and the occupier must return to their own land,” Mr. Zelensky said before finishing with the historical national saying that has become a defiant mantra since the war began: “Slava Ukraini,” or “Glory to Ukraine.”

The panel is one of the many events taking place this week on the sidelines of the U.N. General Assembly. China has sent a vice president, Han Zheng, to the Assembly rather than its top diplomat, Foreign Minister Wang Yi.

The panel is expected to have five speakers, including Rayhan Asat, an advocate for Uyghur rights whose younger brother, Ekpar, has been serving a prison term in the Xinjiang region of China after being detained in 2016 and convicted of inciting ethnic hatred; Agn?s Callamard, secretary general for Amnesty International and a former special rapporteur for the United Nations on extrajudicial killings and executions; and Sophie Richardson, China director at Human Rights Watch.

“By intimidating participation from various U.N. missions as a form of reprisal tactic, China seeks to silence the voices of former U.N. mandate holders and top experts from foremost human rights organizations who bear witness to China’s relentless atrocities,” Ms. Asat said.

“I urge global leaders, including the U.N. secretary general, to discern these patterns of human rights abuses, listen to our analysis, and take decisive action to end the atrocities against the Uyghurs,” she added.

The Uyghurs are a Turkic-speaking and mostly Muslim ethnic group that for centuries lived in oasis towns along the Tarim Basin and in the Ili Valley of Xinjiang. China has taken measures to try to control them, including detaining many in internment camps. In January 2021, Secretary of State Mike Pompeo said the State Department had determined the Chinese government was committing genocide in Xinjiang.

The Chinese mission to the United Nations did not respond to an email seeking information about its letter, which was initially reported by National Review.

Ms. Asat said officials from the governments of the United States, the European Union and Germany were all expected to deliver remarks at the panel.

His frustrations with big country leaders came through too. “Every country is feeling the heat but I’m not sure our leaders are feeling the heat,” he said.

These are notable word choices. Many powerful leaders, including officials in the Biden administration, acknowledge the need to capture and store the planet-warming gases produced by fossil fuels, but stop short of endorsing a phaseout of fossil fuels.

Mr. Guterres linked the climate crisis to other “existential” threats by opening his speech with the Libyan floods. The people of Libya, he said, are “victims of years of conflict, victims of climate chaos, victims of leaders near and far” who failed to bring peace.

He is correct. Human-made climate change, driven by the burning of fossil fuels, made the Libyan floods 50 times more likely, according to a study by a group of scientists with World Weather Attribution.

He is also expected to promote his administration’s achievements around the globe amid growing resistance to additional Ukraine aid, a looming government shutdown, inflation and listless approval ratings.

Ahead of the 2024 presidential election, with Mr. Biden effectively tied with former President Donald J. Trump in early polling, many other nations will be greeting the president with uncertainty about his staying power.

“He will lay out for the world the steps that he and his administration have taken to advance a vision of American leadership that is built on the premise of working with others to solve the world’s most pressing problems,” said Jake Sullivan, the president’s national security adviser.

“The president will talk about how those steps — how all of those steps he’s taken so far ladder up to a larger vision.”

At the United Nations this week, Mr. Biden will also argue that the same nations that came together to oppose Russia’s invasion of Ukraine need to focus their attention on and do more to support the desperate economic fates of some of the world’s poorest countries, many of them in the southern hemisphere.

This week, Mr. Guterres, a seasoned politician from Portugal now in his second and last term as the head of the United Nations, is trying a new diplomatic wink-and-nod tactic. He is hosting a summit on Wednesday at which countries that have accelerated their plans to phase out fossil fuels are being invited to speak, and only if they send cabinet-level or more senior leaders. To show that they take the summit seriously.

“A naming and shaming device that doesn’t actually require naming and shaming anyone,” said Richard Gowan, an analyst with the International Crisis Group.

First Avenue will be closed along the U.N. complex, between 42nd and 48th streets, the New York City Police Department said, as will a number of side streets on the East Side. Dedicated cone lanes were created to provide speedier routes for emergency vehicles and for dignitaries traveling to and from the Assembly.

Subway trains will continue to run about every three minutes during rush hour, the Metropolitan Transportation Authority said, urging riders to take advantage.

“The fastest and safest way to get around the East Side of Manhattan during the United Nations General Assembly is by taking one of the numerous subway lines that provide round the clock service,” said Richard A. Davey, the president of New York City Transit.

Increased security will lead to changes in multiple bus routes, the M.T.A. said.

Bike lanes on First Avenue and Second Avenue, which are used by 7,000 bicyclists every day, will remain open, according to the city’s Transportation Department, which has deemed each day this week a “Gridlock Alert” day, signaling that they are among the most congested traffic days of the year.

Protests organized around various causes were also expected to disrupt the surrounding areas. The Police Department said it planned to dispatch officers throughout the city to keep the week’s events safe and running smoothly.

Edward A. Caban, the police commissioner, said at a news conference last week that there were “no credible threats to the U.N. General Assembly or New York City in general.”

Several hundred police officers and traffic agents will staff security checkpoints throughout Midtown, Mr. Caban said.

The department’s aviation unit, harbor patrol and K-9 units will all be deployed, he added. Secret Service agents and members of the Diplomatic Security Service will also be on the ground.

President Biden is scheduled to speak at the Assembly on Tuesday, as is President Volodymyr Zelensky of Ukraine.

Here is how the Assembly works.

What does the General Assembly do?

The General Assembly is one of six bodies in the United Nations, including the Security Council and the Economic and Social Council.

The body was established in 1945 as “the main deliberative, policymaking and representative organ” of the U.N., and it is the only one within the U.N. and the wider world of international alliances (NATO, BRICS and the Group of 20, for instance) in which all 193 member states have equal representation. As a condition of membership, each state must pay an “assessed contribution” to the operations of the U.N.

“It is the place where every country has a seat,” said Peter J. Hoffman, an associate professor of international affairs at the New School and the director of its United Nations Summer Study. “It’s tough to herd the cats, but the fact that everybody is in the room together and everybody has an opportunity, that in itself creates a sort of credibility for it.”

At the meeting in New York, representatives from each member state discuss international issues as part of the General Debate and vote on hundreds of resolutions.

What are the Assembly’s powers?

Unlike the U.N. Security Council, which can impose sanctions or authorize the use of force, the General Assembly is purely deliberative. Much of its power is derived from its ability to address issues and make recommendations on matters of international importance.

“In terms of actual resolutions with teeth, that’s never going to happen because when the Security Council issues a resolution, it says, You will do this,” Dr. Hoffman said. “When the General Assembly does it, it’s a recommendation: You should do this.”

For instance, a resolution the Assembly passed in November 2022 allowed for the United Nations’ first commemoration in May this year of Palestinian displacement during the creation of Israel.

The General Assembly also appoints the U.N. secretary general, currently Ant?nio Guterres, for five-year terms and the Security Council’s 10 nonpermanent members. A new president of the Assembly is elected every year, and the position rotates among representatives of five geographic regions: Africa, Asia and the Pacific, Eastern Europe, Latin America and the Caribbean, and Western Europe and others.

The Assembly meeting gives leaders a global platform. During the General Debate, each member state is allotted 15 minutes to speak on the year’s theme, but that limit is generally disregarded. Last year, President Volodymyr Zelensky of Ukraine delivered a searing rebuke of the Russian invasion of his country in a recorded address to the General Assembly.

What is on this year’s agenda?

The full theme for 2023 is “Rebuilding trust and reigniting global solidarity: accelerating action on the 2030 agenda and its Sustainable Development Goals toward peace, prosperity, progress and sustainability for all.” But the key words are “2030 agenda” and “Sustainable Development Goals.”

In 2015, the General Assembly adopted 17 objectives, collectively known as the Sustainable Development Goals, or S.D.G.s, as part of “a shared blueprint for peace and prosperity for people and the planet, now and into the future.” They include “no poverty,” “zero hunger,” “climate action” and “gender equality,” among others.

The S.D.G.s were formally adopted under a resolution known as Agenda 2030, a reference to when some of them should be achieved, though some goals have no due date. In 2017, a resolution was passed to formalize specific indicators of progress on these goals.

“The real story is that only 15 percent of the S.D.G.s have been met and about half of them are off track,” Dr. Hoffman said.

In an effort to nudge the body, Mr. Guterres issued “a wake-up call to speed up implementation of the S.D.G.s. Member states have been given until 2024 to figure out a way to get the S.D.G.s and Agenda 2030 back on track.

How has the Assembly changed over the years?

Since its establishment, the U.N. General Assembly has grown to 193 member states as of 2011, when South Sudan was admitted, from 51 nations primarily based in Europe, the Americas and the Middle East.

The U.N.’s founding coincided largely with the advent of the Cold War, which then created a wedge between the West and the East, primarily on the Security Council. But the politics of the Assembly have long been dictated by tensions between the wealthy nations of the “global north” — broadly considered to include Australia, Europe, North America, Israel, Japan, South Korea and New Zealand — and the “global south,” largely represented by former colonies of the global north across Africa, Asia and Oceania, Latin America and the Caribbean.

“By the ’60s and ’70s, you really start to see the politics change and particularly the emergence of what was called the new international economic order in the ’70s,” Dr. Hoffman said, “with a proposal basically among global south and nonaligned countries to say, Oh, the terms of the trade are really unfair between the north and the south.”

At the same time, pressure on the global south to begin addressing the destruction of the environment spurred a blistering response in a 1972 speech by Prime Minister Indira Gandhi of India at a U.N. conference in which she asked, “Are not poverty and need the greatest polluters?” as a statement on what she saw as the hypocrisy of the global north in dictating terms to developing countries.