It is unclear how long the S.D.F. — a Kurdish-led group that has managed in recent months to attract a more diverse coalition, including Arabs and Assyrians — can maintain control over its areas. The Trump administration does not appear to have a plan to reconstruct the areas or defend them for long after the battle against Islamic State ends. Without United States air support for the rebels, the Syrian government is likely to retake the territory.

The government, led by President Bashar al-Assad, controls around 60 percent of the country and has vowed to retake the rest of it.

Still, a Kurdish official, reached by phone in Qamishli, a Kurdish-controlled city in the northeast, was ecstatic. Speaking on the condition of anonymity because he was not authorized to discuss politics, he noted that the S.D.F. now controls Syria’s largest hydroelectric dams and oil fields as well as sprawling gas fields and agricultural lands.

That, he said, could give Kurds and their allies leverage to get a seat at the table in any future peace talks. Up to now, they have not been recognized as a party to the long-stymied talks held in Geneva between the Syrian government and a coalition recognized by the United States and its allies as the sole representative of the Syrian opposition.

The capture of the Omar oil field could also be an economic boon for the area controlled by the S.D.F. Fuel already sells in its territories at a fraction of the cost as in government-held areas. Now, the Kurdish official said, the local administration could sell the oil not only in its own territory, but also in other areas that Mr. Assad does not control, enlarging its economic base.

A member of an Arab tribe who fled his home in the eastern Syrian city of Mayadeen this month when fighting intensified between the Islamic State and government forces there, and who requested anonymity to avoid reprisals, said he hoped the S.D.F. and Kurds would be more equitable with the reserves than the Syrian government had been.

The man, Riad, a schoolteacher, said the government had given local Sunni Arab tribe members like himself mainly low-level jobs, saving well-paid ones for government cronies and leaving locals to deal with the environmental problems from the industry.

He said that pro-government forces had looted his city when they retook it from the Islamic State. Although he said he did not completely trust the Kurds, he said that at least the S.D.F. had some local tribesmen among its fighters, so the area could get some benefits.