“It’s better to have a conversation to engage than not to do so just because the world is blowing up in so many places,” said Angela E. Stent, head of the Russia studies program at Georgetown University and a former national intelligence officer on Russia. “Not to meet with him would be sending a signal that we don’t think there’s anything to talk about in terms of cooperation on Syria.”

But it would be a turnaround of sorts for Mr. Obama, who has worked assiduously to isolate Mr. Putin for his violations of Ukrainian sovereignty. “Mr. Obama can expect nothing positive to come from seeing Mr. Putin,” said John Herbst, a former ambassador to Ukraine who is now at the Atlantic Council in Washington. “Meeting with the Russian strongman would only make the president look weak.”

In Moscow, analysts said Mr. Putin wants to use a speech he will deliver at the United Nations to shift away from the Ukraine crisis by pressing the case for an international coalition against the Islamic State that includes Mr. Assad’s government.

“The Kremlin has far-reaching goals for that speech,” Aleksandr Golts, a military analyst, wrote in The Moscow Times. “It hopes that the process of forming such a coalition would free Russia from its international isolation caused by its annexation of Crimea and the war in eastern and southern Ukraine and also make it a respected member of the world community again.”