This week kicks off the high-level part of the U.N. General Assembly, when world leaders meet to discuss the world’s most pressing problems. It is the 80th year of the gathering, and comes at a difficult time for the organization, with wars raging globally and a budget crisis internally. Yet it remains a big stage, with more than 140 world leaders and senior officials and delegations converging on New York.

The General Debate, which will start on Tuesday, is the main event, when representatives from each member state will speak on various issues.

Beyond the main debate, there are other events the world may be keeping tabs on:

• On Monday, Palestinian statehood is due to take center stage at a conference hosted by France and Saudi Arabia. Australia, Britain, Canada and Portugal said on Sunday that they now formally recognized Palestinian statehood, and France has announced its intention to do so.

  Also, the Security Council is expected to hold an emergency meeting on the recent incursion by Russian fighter jets into Estonian airspace.

• On Tuesday, the Security Council is expected to hold a meeting on the war in Gaza and the security situation in the Middle East (scheduled for 1 p.m. Eastern) and another on Ukraine (scheduled for 4 p.m. Eastern).

• On Wednesday, leaders are expected to gather for a climate summit to present commitments to tackle climate change and discuss solutions.

• On Thursday, leaders are expected to discuss artificial intelligence.

The high-level gathering also offers world leaders opportunities for one-on-one meetings. António Guterres, the U.N. secretary general, has expressed interest in meeting with President Trump. The Russian foreign minister may meet with his U.S. counterpart as well, after diplomatic efforts between Moscow and Washington last month seemed to do little to slow the war in Ukraine.

Here’s a day-by-day breakdown of some of the speakers to watch out for.

Tuesday, Sept. 23

Following a decades-long tradition, Brazil’s president, Luiz Inácio Lula da Silva, is set to open the comments from member states. This month, Jair Bolsonaro, the country’s former president, was sentenced to more than 27 years in prison for overseeing a failed coup plot after losing the 2022 election. Mr. Trump had urged Brazil to drop the charges, and Mr. Lula has vowed not to bend to U.S. pressure.

Mr. Trump is to come next, speaking on behalf of the United States, following convention for the host country to speak second. It is not known what he will say, but he could touch on topics including the wars in Gaza and Ukraine, two conflicts he has pledged to end, so far without success; an escalating immigration crackdown at home; and a wave of tariffs intended to protect American industries that has alarmed trading partners around the globe.

The General Assembly is expected to hear from the Turkish president, Recep Tayyip Erdogan, in addition to leaders from Jordan, Qatar and Egypt. Israel conducted an airstrike in Qatar this month that targeted Hamas officials, a move that drew outrage from some Arab leaders.

The chamber is also due to hear from the president of France, Emmanuel Macron, who is leading a diplomatic push for recognition of Palestinian statehood in an effort to salvage a two-state solution with Israel.

President Karol Nawrocki of Poland, whose country has raised alarm over a recent incursion of Russian drones, is to speak in the afternoon.

So will Claudia Sheinbaum, Mexico’s first female president. Her country is facing pressure from Mr. Trump to accommodate American interests on trade and combat drug cartels.

Wednesday, Sept. 24

Ukraine’s president, Volodymyr Zelensky, is scheduled to speak, almost certainly about Russia’s invasion of his country. Mr. Zelensky expressed cautious optimism after meeting with Mr. Trump in August, but the prospect of a meeting with President Vladimir V. Putin of Russia remains elusive, and Moscow has stepped up its drone attacks.

Iran’s president, Masoud Pezeshkian will attend, according to a statement posted to social media by his political adviser. His remarks would come after a war with Israel in June, which dealt a heavy blow to his country’s military chain of command.

Wednesday is also expected to be the U.N. debut of Syria’s new president, Ahmed al-Shara, after a rebel alliance he led ousted the strongman Bashar al-Assad in December.

Thursday, Sept. 25

The Trump administration denied visas to Mahmoud Abbas, the president of the Palestinian Authority, and his delegation, but the General Assembly voted overwhelmingly to permit Palestinian representatives to participate virtually, including with a prerecorded statement from Mr. Abbas. Israel’s ground operation in Gaza City has deepened a humanitarian crisis in the enclave, where hunger is rampant.

Prime Minister Kamil Idris of Sudan, according to the Sudanese news media, is expected speak on Thursday, too. A civil war has engulfed his country for two years.

Friday, Sept. 26

Prime Minister Benjamin Netanyahu of Israel is due to start off the speeches on Friday morning. Mr. Netanyahu faces a rift with his country’s military leadership over his war strategy in Gaza. The war has also deepened his isolation internationally and increased his political opposition domestically.

He is to be followed by Premier Li Qiang of China, Prime Minister Keir Starmer of Britain and India’s minister of external affairs, S. Jaishankar. The close ties India’s prime minister, Narendra Modi, one enjoyed with Mr. Trump have frayed in recent months.

There may be comments from a representative of Nepal, where days of violent protests this month toppled the government. The country’s first female chief justice and now leader, Sushila Karki, has assumed the role of interim prime minister. The country’s previous prime minister had been planning to attend, according to Nepali news media; it is unclear who is going now.

Saturday, Sept. 27

Prime Minister Mark Carney of Canada is expected to speak on Saturday. Mr. Carney has met with Ms. Sheinbaum to devise an “action plan” for dealing with Mr. Trump’s tariffs. Russia’s foreign minister, Sergey V. Lavrov, is expected to also deliver remarks in the first half of the day. The Kremlin has insisted that it obtain its own “security guarantees” before laying down arms in Ukraine.

Venezuela’s foreign minister, Yvan Gil, is expected to address the Assembly on Saturday, amid a major buildup of U.S. naval forces outside Venezuela’s waters. Washington has sharpened its language about fighting drug cartels, made deadly strikes on boats carrying people accused of being drug smugglers and labeled President Nicolás Maduro of Venezuela a terrorist-cartel leader. Mr. Maduro has repeatedly accused the United States of trying to topple him.

Monday, Sept. 29

Remarks from representatives of Afghanistan, where the Taliban returned to power four years ago, and South Sudan are due to end the week. It is unclear who will represent each country.