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.”

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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.

Moscow has assured the United States that the government of President Bashar al-Assad of Syria will abide by the agreement, the official said. The assent of the government in Damascus came even though the United States continues to insist that neither Mr. Assad, nor any member of his family, can have a long-term role in the country’s leadership.

News of the agreement was first reported by The Associated Press.

The United States and Russia agreed to similar cease-fires last year, all of which quickly disintegrated. But Mr. Tillerson said there were reasons to believe that this latest attempt would not only hold, but could serve as a model for cease-fires elsewhere in Syria.

He said the defeat of the Islamic State was within sight, and negotiators were discussing what comes next. Mr. Tillerson also said war fatigue — after six years of conflict — was helping speed potential agreements.

“In many respects, people are getting tired. They’re getting weary of the conflict,” Mr. Tillerson said.

Sergey V. Lavrov, the Russian foreign minister, later said the cease-fire would take effect from midnight to noon local time on Sunday in the areas of Daraa, Quneitra and Sweida in Syria along the Jordanian border. “At first, security around this de-escalation zone will be guaranteed by the forces and means of the Russian military police, in coordination with the Americans and Jordanians,” he said.

But the senior State Department official disputed that, saying the parties had yet to agree on monitoring. The official said the cease-fire was, at best, a modest advance in ending the conflict. Still, southwestern Syria has experienced far less violence than in other parts of the country during the war, so the areas the cease-fire will cover is by no means at the heart of the conflict.

Mr. Tillerson said that Mr. Trump and Mr. Putin spent much of their more than two hour meeting discussing the Syrian conflict.

“And I would tell you that, by and large, our objectives are exactly the same. How we get there, we each have a view,” Mr. Tillerson said. “But there’s a lot more commonality to that than there are differences. So we want to build on the commonality, and we spent a lot of time talking about next steps.”

Mr. Tillerson conceded that the United States may not have all the answers.

“Maybe they’ve got the right approach and we’ve got the wrong approach,” he said in an extraordinary concession, considering previous statements by Mr. Trump that Russia likely had prior knowledge of a Syrian chemical attack on its own people.