However, AP reported that a ceasefire would take effect on Sunday at noon Damascus time.
A fourth de-escalation zone in southern Syria has also been considered, but it needs the involvement of other countries, such as the U.S. and Jordan, who have influence in the region. The statement came as Trump prepared to meet with Putin on Friday in Germany and as the USA seeks to consolidate gains made against the Islamic State in recent weeks and prepare for a post-IS group future.
The Trump administration has grappled with a strategy on how to deal with Syria once Islamic State is pushed out of its territory.
Lavrentyev also said Russian Federation has called on member countries of the Commonwealth of Independent States to consider providing military observers for the potential de-escalation zones.
The three countries have been successfully mediating talks between the Syrian government and opposition in the Kazakh capital of Astana since January.
However, the US-led coalition has used the opportunity to establish their own so-called "de-confliction" areas, within which, it has on several occasions, used perceived threats to allies as a pretext to strike Syrian government forces.
Tillerson said the USA and Russian Federation have "unresolved differences" on various issues, but also the potential for cooperation.
In the unusual statement, Tillerson also insisted America's top priority in Syria remains defeating the Islamic State terrorist network and that the future of the Syrian regime of Bashar Assad, who is engaged in a civil war with rebel factions, must be decided through a political settlement.
Tillerson said the difference this time is Russia's interest in seeing Syria return to stability. Up to now, Assad has rejected any proposals that would see him leave power, contributing to an impasse that has prolonged Syria's suffering. It was reported last month that Mr McGurk and US Syria envoy Michael Ratney held secret talks with Russian Federation in Jordan in May. Russia's plan stipulates that "guarantors"-Russia, Turkey, and Iran for now-and agreed-upon partners on the ground should fight these irreconcilables".