 -- The U.S. and Russia, along with the Kingdom of Jordan, have agreed to a cease-fire in southwest Syria, Secretary of State Rex Tillerson announced at an off-camera briefing at the G-20 summit.

The cease-fire, which begins on Sunday, July 9, at noon Damascus time, is the result of months of behind-the-scenes negotiations that started at the beginning of the Trump administration and apparently has the support of both the Assad regime and the main rebel group in the area, according to a senior State Department official.

Tillerson praised the announcement as a first step in U.S.-Russian cooperation on Syria, where he said the countries have the same goals. “This is our first indication of the U.S. and Russia being able to work together in Syria,” he said, adding later, “Russia has the same, I think, interests that we do in having Syria become a stable place, a unified place.”

The U.S. side has declined to say who will enforce the cease-fire, saying more meetings are scheduled in the next week to work out the details, but Tillerson added that the three countries have a very clear picture of who will provide security forces. At a separate press conference, Russian Foreign Minister Sergey Lavrov said it would be Russian military police enforcing the agreement, with close U.S. and Jordanian coordination.

Lavrov also noted there are three de-escalation zones in three Syria provinces –- Daraa, as-Suwayda and Quneitra –- where the cease-fire will be implemented. Tillerson would only describe the area as located in southwest Syria and important to Jordan’s security, as well the Syrian battlefield.

Southern Syria is mainly divided between the regime of Syrian President Bashar al-Assad, backed by Russia, and a coalition of rebel forces known as the Southern Front, with a small pocket of ISIS-aligned fighters. The Russians will use their "influence" to guarantee Assad and his allies abide by the cease-fire, while the U.S. and Jordan are supposed to deliver the rebels.

"The basis of the whole understanding is that each side uses its influence with those parties on the ground with which we have relationships," said the senior official. While the U.S. does not have troops in this part of the country, it is in close touch with the Southern Front.

"They themselves were supportive of a cease-fire," the senior official added, arguing they are "dreadfully tired of the violence and looking for an opportunity for a credible cease-fire, an enduring cease-fire to be implemented."

The hope here is to lock in the current battlefield lines between the rebels and Assad, an agreement reached just last week. Neither side is supposed to use the cease-fire to gain an advantage, focusing instead on killing the remaining jihadis. But it was the three outside parties that have agreed to these particular lines of conflict, and it remains to be seen if the warring parties on the ground will as well.

After the cease-fire agreement, U.S. President Donald Trump and Russian President Vladimir Putin had a “lengthy discussion” about other areas in Syria where the two sides hope to continue to work on “de-escalating” and working toward a political process to secure the future of the Syrian people, according to Tillerson.

"We're hoping we can replicate that elsewhere," he added. The senior State Department official added that they are realistic about its chances, but they wanted to begin with a "more manageable part" of the war-torn country using a “narrow scope” and “fairly modest ambitions” to lay the groundwork for real de-escalation zones in the southwest and maybe eventually for greater cooperation elsewhere.

When asked why the U.S. has confidence a cease-fire will succeed this time after multiple failures in the past, Tillerson said what’s different now is “the level of commitment on the part of the Russian government” and “where we are relative to the whole war against ISIS.”

Both countries are looking ahead to how to stabilize Syria, he said, with the fight against ISIS “progressing rapidly.”

"We felt as we got into these discussions that it was worth trying," added the senior official. Russia "clearly expressed an interest in pursuing it. They expressed a willingness and an ability to hold up their end of the bargain, that is of course to use their influence on principally the regime, so it opened the door to at least creating what we've done today, which is an opportunity to test the proposition. It's worth testing."

But there remains one other big disagreement between the two countries: Tillerson noted that the U.S. still sees no role for Assad or the Assad family.

“We've made it clear to everyone, we've certainly made it clear in our conversations with Russia, that we do not think Syria can achieve international recognition in the future -- even if they work through a successful political process -- the international community simply is not going to accept a Syria led by the Assad regime,” he said.

Russia is a longtime ally of the Assad regime, and Russian military forces have boosted the brutal dictator's standing on the battlefield, over the six years since the country's civil war began.

Tillerson made no mention of Assad’s alleged war crimes, but said if Syria wants security, an economically viable future, humanitarian aid and reconstruction assistance, Assad would have to go. How he leaves could be determined later, but the political process should include a transition away from the Assad family, he added.