WASHINGTON — The United States, Russia and Jordan have agreed to foster a cease-fire in a limited area of southwestern Syria that will begin at noon on Sunday, Secretary of State Rex W. Tillerson said on Friday after the first face-to-face meeting between President Trump and President Vladimir V. Putin of Russia.

The agreement came after months of negotiations among the three countries. A senior State Department official who was involved in the talks said important pieces of the deal remained to be hammered out in the coming days, including who would monitor and enforce the pause in violence.

“I think this is our first indication of the U.S. and Russia being able to work together in Syria,” Mr. Tillerson told reporters on Friday night in Hamburg, Germany, after the more than two-hour meeting between Mr. Trump and Mr. Putin. “And as a result of that, we had a very lengthy discussion regarding other areas in Syria that we can continue to work together on to de-escalate the areas and violence once we defeat ISIS, and to work together toward a political process that will secure the future of the Syrian people.”

The agreement hinges on a boundary line — as set by the United States, Russia and Jordan — between areas of control for the warring forces and state proxies, the State Department official said. But outlawed factions — including Al Qaeda — could refuse to abide by the agreement and even actively work to undermine it, the official said.