He said by videoconference from Geneva that it's time to move on the political track to end the Syrian conflict and "now is the moment of truth".
Syria and its opposition will engage in a new round of talks at the end of next month, the UN's envoy to Syria announced Thursday.
"The reign of the Assad family is coming to an end", Tillerson said on October 26 after meeting in Geneva with the United Nations' Syria envoy, Staffan de Mistura.More news: Growth Analysis of Mylan NV (MYL)
Russia-backed Syrian government forces as well as US -backed, Kurdish-led troops have recently significantly reduced territory controlled by Daesh across Syria.
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 the only reason Assad's forces had succeeded in turning the tide in the more than six-year war was "air support they have received from Russia".More news: INTERCONTINENTAL EXCHANGE, INC. (NYSE:ICE) Files An 8-K Regulation FD Disclosure
Tillerson said Iran, Assad's other main ally, should not be seen as having made the difference in the defeat of Islamic State in Syria.
He downplayed remarks by some critics that recent government battlefield gains represent a "triumph" for Iran. "Iran has not been successful; the Russian government has been more successful".
Staffan de Mistura told the Security Council on Thursday that he hopes a meeting in Kazakhstan's capital Astana on October 30-31 co-sponsored by Turkey, Iran and Russian Federation will "prevent further unraveling of interim de-escalation and cease-fire arrangements" in Syria.More news: Oasis Petroleum Inc. (OAS)
"I see Iran as a hanger-on", Tillerson said.
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