Tillerson's comments late Wednesday come ahead of a highly anticipated meeting between US President Donald Trump and Russian President Vladimir Putin this week at the G20 summit in Germany, in which the two leaders are expected to discuss the Syrian conflict.
Israel also is part of the agreement, one USA official said, who like others wasn't authorized to speak publicly on the matter ahead of Tillerson's official announcement and demanded anonymity.
The Syrian conflict has expanded into a war that involves regional and world powers - including the U.S., Russia, Iran, Turkey, Saudi Arabia, and Qatar - whose interests sometimes overlap, but at other times lead to multiple confrontations and uncomfortable alliances. The U.S., wary of Iran's involvement, was not a part of that deal.
Tensions between the us and Russian Federation reached a boiling point in mid-June after a U.S. F/A-18E Super Hornet shot down a Syrian Air Force Su-22 that bombarded coalition-backed Syria Democratic Forces fighters outside the established deconfliction zone of Ja'Din.
US, Russia Agree on Ceasefire in Southwestern Syria
Two days later, the Pentagon announced it had shot down an Iranian-made drone in the country's south-east, where American personnel have been training anti-Islamic State fighters, and where a complex geopolitical battle is unfolding.
Obama wanted to limit America's involvement in Syria's civil war.
In March, Tillerson said the United States would set up "interim zones of stability" to help refugees return home in the next phase of the fight against Islamic State and al Qaeda in Syria and Iraq. Tillerson said on Wednesday that Russian Federation has a responsibility to prevent Assad's government from conducting further chemical weapons strikes.
Tillerson said all the parties in Syria, especially Russian Federation, "must ensure stability on the ground", to prevent ISIS "from rising anew".
Mr Tillerson said: "We see no long-term role for the Assad family or the Assad regime,", while a U.S. 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". "Russia is neither capable nor willing to give us what we want in Syria", Lister said. "Lastly, Russia has a special responsibility to assist in these efforts".
The head of Syria's negotiation team, Bashar Ja'afari, held Ankara responsible as he stated that the Turkish delegation approach towards the process "has been a negative policy", which is different from "the positive start point taken" by all the other parties. Trump's administration has approached the notoriously strained relationship by trying to identify a few limited issues on which the countries could make progress, thereby building trust for a broader fix of ties.