Russia’s leader hosted his Turkish counterpart as a U.S.-brokered ceasefire with Kurdish forces came to an end, underscoring Moscow’s emergence as a powerful player in the Middle East.

By Anton Troianovski and Patrick Kingsley

SOCHI, Russia — His jets patrol Syrian skies. His military is expanding operations at the main naval base in Syria. He is forging closer ties to Turkey. He and his Syrian allies are moving into territory being vacated by the United States.

And on Tuesday, President Vladimir V. Putin of Russia played host to President Recep Tayyip Erdogan of Turkey, for more than six hours of talks on how they and other regional players will divide control of Syria, a land devastated by eight years of civil war.

The negotiations ended with a victory for Mr. Putin: Russian and Turkish troops will take joint control over a vast swath of formerly Kurdish-held territory in northern Syria, in a move that cements the rapid expansion of Russian influence in Syria at the expense of the United States and its Kurdish former allies.

Under the terms of the agreement, Syrian Kurdish forces must now retreat more than 20 miles from the border, abandoning land that they had controlled uncontested until earlier this month — when their protectors, the American military, suddenly began to withdraw from the region.

Mr. Putin has emerged as the dominant force in Syria and a major power broker in the broader Middle East — a status showcased by Mr. Erdogan’s hastily arranged trip to the president’s summer home in Sochi. And it looks increasingly clear that Russia, which rescued the government of President Bashar al-Assad of Syria with brutal airstrikes over the last four years, will be the arbiter of the power balance there.

As President Trump questions American alliances and troop deployments around the world, Russia, like China, has been flexing its muscles, eager to fill the power vacuum left by a more isolationist the United States. In Syria, both Mr. Putin and Mr. Erdogan see opportunity in Mr. Trump’s sudden withdrawal this month of American forces in the country.

Mr. Erdogan had long wanted go to war against the Kurdish-led forces that control northeast Syria, but he dared not, as long as the Kurds’ American allies were stationed there, too. He responded to Mr. Trump’s withdrawal by launching an invasion.

Tuesday’s meeting began hours before the end of an American-brokered truce between Turkish and Kurdish forces in Syria, where Mr. Erdogan says his troops have seized more than 900 square miles of territory since invading on Oct. 6.

“The U.S. is still the 500-pound gorilla,” said Howard Eissenstat, a professor of Middle East history at St. Lawrence University. “If the U.S. decided that ‘issue X’ was a primary concern to its national security, there would be very little that anybody in the region could do about it.”

But with the United States increasingly removing itself from the picture — as symbolized in the Russian news media by the images of abandoned washing machines and unopened cans of Coca-Cola left behind in the chaotic withdrawal — it was Russia whose consent Mr. Erdogan needed on Tuesday to consolidate and extend his gains.

“Before, Turkey could play the U.S. against Russia and Russia against the U.S.,” said Sinan Ulgen, chairman of the Center for Economics and Foreign Policy Studies, an Istanbul-based research group. “Now that’s no longer the case, and Russia has shaped up to be Turkey’s only real counterpart in Syria.”