Announcing that he will convene the eighth round of intra-Syrian talks on 28 November in Geneva, the United Nations Special Envoy for Syria on Thursday urged all stakeholders to seize the opportunity to find a solution to the crisis plaguing the war-torn country.
Tillerson, who is now in Geneva, made the remarks after he met with UN Syria envoy Staffan de Mistura.
Seven rounds of talks have achieved only incremental progress toward a political deal, with negotiations deadlocked over the fate of Syrian regime head Bashar al-Assad. The United States generally sends an observer to Astana.
America's top diplomat said that an exit of Assad should be done through the Geneva process led by de Mistura, but that such a departure was not a "prerequisite" for that process to start.
Tillerson said that the USA wants Syria to remain unified as part of a peace agreement, but that there must not be a role for Assad in the government.
Russian President Vladimir Putin said that more than 90 percent of Syria's territory had been recaptured from "terrorists".
He said the only reason Assad's forces had succeeded in turning the tide in the war against Islamic State and other militants was "air support they have received from Russia".
Putin generally does not differentiate between IS fighters and US -backed rebels when referring to "terrorists". "Iran has not been successful; the Russian government has been more successful".
He downplayed remarks by some critics that recent government battlefield gains represent a "triumph" for Iran.
"Applying this logic, my considered assessment as the mediator is that, for round eight - and I would like to ask you for your support on this - we should see if we can move some aspects of the agenda concretely forward - just far beyond exploration, and into negotiation", he added, noting also that a serious step on detainees, abductees and missing persons is needed. We have had success. "I don't think that Iran should be given credit for the defeat of ISIS in Syria".
More than 330,000 people have died and millions have been driven from their homes in the conflict in Syria.