Secretary of State Rex Tillerson (fifth from left) and other foreign ministers meet at the United Nations for a discussion on Syria on Monday, Sept. 18, 2017. (Stephanie Keith/Reuters)

The Islamic State is rapidly losing control of territory in Syria, but donor countries will not reconstruct the war's damage until a "credible" political process emerges from negotiations, a senior U.S. official said Monday.

David Satterfield, the State Department's acting assistant secretary for Near East affairs, told reporters that was the consensus of diplomats from 17 countries and organizations from Europe and the Middle East who met with Secretary of State Rex Tillerson to discuss Syria on the sidelines of the United Nations General Assembly.

Satterfield said the war against the militants in Syria and Iraq is progressing faster than anticipated.

"The defeat of ISIS is underway," he said, using an acronym for the Islamic State.

"We are all committed to humanitarian aid," he added. "And that will continue to flow, of course. But the reconstruction of Syria depends very much on that credible political process."

Their biggest lever, Satterfield said, is that without a political process, "you're not going to get the kind of investment by the international community that's really necessary for the reconstruction of Syria."

The coalition that met in New York does not include Russia, which has troops in the country and backs Syrian President Bashar al-Assad.

Earlier Monday, the Russian Defense Ministry said Syrian and Russian forces had crossed the Euphrates River near the Islamic State stronghold of Deir el-Zour and forced out militants. It said the troops were heading east and "broadening the seized foothold."

Their advance could lead to a confrontation with the U.S.-backed Syrian Democratic Forces, whose fighters have waged a separate offensive against the Islamic State. Two days earlier, the SDF said Russian airstrikes hit its fighters, which Russia denied.

Satterfield noted the United States and Russia have lines of communications known as "deconfliction," through which they try to avoid faceoffs.

"We're engaged in working with Russia, deconfliction with Russia, as we each move on defeating ISIS," he said. "It's not a rivalry. It's not a contest."