Tillerson told reporters on Thursday that the reign of the Assad family was "coming to an end" after what he called a "fruitful" discussion with UN Syria envoy Staffan de Mistura, who later addressed the UN Security Council by videoconference.
"The US wants a whole and unified Syria with no role for Bashar Assad in the government," Tillerson said. "The only issue is how that should be brought about."
But Assad's exit was not a "prerequisite" for the talks to start, Tillerson said.
Staffan de Mistura is expected to reconvene UN-mediated intra-Syrian talks on November 28. This comes after gains on the battlefield by Assad's Russian-backed forces.
These will be the eighth round of talks under his guidance since early 2016.
Opposition delegations — which do not include the so-called "Islamic State" (IS) or other UN-designated terrorist groups — have never spoken directly with Syrian government envoys under de Mistura's mediation.
No triumph for Tehran
Tillerson also said the Syrian government's advances did not amount to a "triumph" for Iran, a key backer of Assad.
"I see Iran as a hanger-on," Tillerson said. "Iran has not been successful; the Russian government has been more successful. We have had success. I don't think that Iran should be given credit for the defeat of IS in Syria."
Russia-backed Syrian government forces as well as US-backed, Kurdish-led troops have recently led to a significant reduction in territory controlled by IS across Syria.
The US-backed forces recently ousted IS from its capital, Raqqa.
jbh/kms (AP, Reuters)