UNITED NATIONS — The United Nations General Assembly opens on Monday with all eyes on the war in Syria and the twin crises it has helped spawn: the unyielding spread of the Islamic State in Syria and Iraq, and the surge of refugees from the region into Europe.

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Leaders of the world’s most powerful nations are due to speak in the morning at the 70th annual General Assembly debate, including President Obama, followed by Presidents Xi Jinping of China, Vladimir V. Putin of Russia and François Hollande of France.

President Hassan Rouhani of Iran, which is among Syria’s most dogged allies, is scheduled to step up to the lectern in the morning as well, along with King Abdullah II of Jordan, whose country is swelling with 630,000 registered Syrian refugees.

Mr. Obama is due to meet with Mr. Putin later on Monday. He is not scheduled to meet with Mr. Rouhani, but they are all invited to a lunch hosted by the United Nations secretary general, Ban Ki-moon, for heads of state and government. The prospect of an Obama-Rouhani handshake is unlikely.

The gathering comes as the war in Syria seems at a pivotal juncture, with Russia increasing its supply of arms to the government of President Bashar al-Assad and Iran insisting, along with Russia, that the fight against terrorist groups take top priority, rather than Mr. Assad’s exit.

Mr. Putin is expected to call for countries around the world to join the effort to rout the Islamic State. That will most certainly be echoed by Mr. Rouhani, who said Sunday night in a meeting with journalists and foreign policy experts in New York that to defeat terrorists, Mr. Assad’s government “can’t be weakened,” according to news reports.

Taken by surprise on Sunday by the announcement of an understanding among Iran, Iraq and Syria to share intelligence about the Islamic State, American officials have so far said only that it is important to “coordinate” their military efforts against the militant group with the Kremlin.

Asked about the Obama-Putin meeting, Jean-Marie Guéhenno, president of the International Crisis Group, said that the situation in Syria had become too sweeping for either leader to ignore much longer.

“They should both recognize that Syria has reached a situation of stalemate, even if the Syrian actors will not acknowledge it, and that the continuation of that stalemate, even apart from the appalling humanitarian consequences of that stalemate, is strategically bad for both countries,” he said. “The more the conflict endures, the more it fragments, the more it radicalizes, the more intractable.”

The General Assembly session will continue Monday afternoon with an address by President Raúl Castro of Cuba, after his country’s historic thaw in relations with the United States. President Muhammadu Buhari of Nigeria, elected this year on a promise to rout Boko Haram extremists from the country’s north, is also expected to give his first address to the General Assembly.

Later Monday, Mr. Obama will lead a summit meeting aimed at strengthening United Nations peacekeeping missions. On Tuesday, a session is set to discuss how to counter violent extremism, including the flow of foreign fighters to terrorist groups. The next day, Russia will host its own Security Council session devoted to counterterrorism in the Middle East.

This week, world leaders will also wrestle with another consequence of the nearly five-year war in Syria: the flow of refugees into Europe. The German foreign minister is to host the world’s most industrialized nations, the Group of 7, to discuss the global migrant crisis, and the secretary general will lead a similar session in the General Assembly.

In Syria, the West’s diplomatic options have been further limited by its failure to stop the flow of foreign fighters into the arms of terrorist groups like the Islamic State and by the Pentagon’s failure to train and equip more than a handful of Syrians to take on the group.

France announced on Sunday that it had carried out airstrikes against what it called Islamic State training camps, even as Mr. Hollande insisted that “the future of Syria cannot be with Bashar al-Assad.”

Britain and the United States have likewise carried out airstrikes against the Islamic State, avoiding, as Russia likes to point out, Mr. Assad’s positions on the battlefield.

The New York Times