Russian President Vladimir Putin and Trump are expected to meet for the first time later Friday on the sidelines of the G20 summit to discuss key issues of the global agenda, including cooperation in the settlement of the Syrian crisis. However, AP reported that a ceasefire would take effect on Sunday at noon Damascus time.
Other details of the agreement weren't immediately released.
The Russians reportedly asked to be responsible for enforcing a cease-fire near the Israeli and Jordanian borders and for policing safe zones that would be established in the region but Israel was adamantly against it and asked that the U.S. be held responsible for monitoring the cease-fire instead, according to Haaretz.
A day later, his Russian counterpart Sergei Lavrov said, "We have asked (for information)".
Tillerson said the United States would also discuss with Moscow joint efforts to implement ceasefires and deliver humanitarian aid.
He said Moscow needs to make sure no faction in Syria "illegitimately re-takes or occupies areas" liberated from Islamic State or other groups.
Before the Trump-Putin meeting, Tillerson signalled that Syria's civil war would be high on the agenda.
Establishing de-escalation zones is a temporary measure and resolving the Syria issue need breakthrough in political settlement, UN Special Envoy for Syria Staffan de Mistura said.
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"We have asked, but we haven't got an answer to the question of what no-fly zones are envisioned, because there has never been any talk of them", Lavrov said during a visit to Paris on July 6.
Russian strategic bombers fired advanced cruise missiles at Islamic State targets in Syria on Wednesday from a distance of 1,000 kilometres (621.37 miles) in a show of force Moscow said demolished three ammunition depots and a command post.
Mr Tillerson said: "We see no long-term role for the Assad family or the Assad regime,", while a USA state department official said "regarding Assad, the United States remains committed to the Geneva process and supports a credible political process that can resolve the question of Syria's future".
The statement made no mention of Assad regime's future.
In a wide-ranging statement, the top USA diplomat said Russian Federation had a "special responsibility" to help create stability on the ground or risk hobbling the fight against the Islamic State group.
The U.S. has been resistant to letting Iran gain influence in Syria - a concern shared by Israel and Jordan, neither of which wants Iranian-aligned troops amassing near their territories.
"Actors in Syria must remember that our fight is with ISIS", Tillerson said. "We see no place for the Assad family in the political future of Syria", added Tillerson.
Russian Federation warned its military would track aircraft from the US-led coalition as potential targets over Syria and suspended a hotline meant to avoid midair incidents after the U.S. downed a Syrian jet last week that had dropped bombs near the US-backed Syrian Democratic Forces.
The deployment of Turkish military units near Kurdish-held areas of northwestern Syria are a "declaration of war", according to the head of the Syrian Kurdish YPG militia on Wednesday, adding that their proximity to Kurdish forces could trigger conflict in a matter of days.