Tillerson proposed that Russian Federation and the United States "explore the possibility" of establishing no-fly zones and other "joint mechanisms" to maintain peace in Syria as the Islamic State loses ground.
"First, parties in Syria must ensure stability on the ground", Tillerson said in a State Department statement.
"If our two countries work together to establish stability on the ground, it will lay a foundation for progress on the settlement of Syria's political future", he said, nudging Russian Federation toward more collaboration despite Putin's deep support for Assad.
The United States launched a retaliatory cruise missile strike days after the onslaught in Khan Sheikhun, targeting a Syrian airbase from where it said the chemical weapons attack was launched.
Tillerson issued the statement on Thursday before heading to the G20 summit in Hamburg, Germany, to join President Donald Trump, where the USA leader will also have his first face-to-face meeting with Russian President Vladimir Putin.
Russian Foreign Minister Sergei Lavrov said Thursday Moscow was seeking to clarify a claim by his U.S. counterpart that Washington is ready to work together to set up "no-fly zones" in Syria.
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She is described by police as an Asian woman, 5 -feet 4-inches tall, 110 lbs., with shoulder length black hair and brown eyes. On Thursday, he took part in a walk with students and university staff to the corner where his daughter was last seen.
After Russia urged global investigators to visit the Shayrat airbase, Mulet said the panel was open to such a mission but would first demand information from Syria on the flight plans at the time of the attack and the commanders in charge.
Russia's proposal may well be the only path to a negotiated settlement between the regime of Syrian leader Bashar al-Assad and the Sunni Arab opposition, but the safe zones are far from ready for the return of refugees.
Mr Tillerson said the U.S. is also open to jointly setting up a truce monitoring and humanitarian aid delivery mechanism.
"The USA and Russian Federation must publicly commit to protecting civilians in Syria and to ending violations by their own forces as well as by the warring parties on the ground".
He said Moscow needs to make sure no faction in Syria "illegitimately re-takes or occupies areas" liberated from Islamic State or other groups.
US -backed forces have surrounded Daesh stronghold in Syria, the city of Raqqa. "And I think that's the most important part of this meeting is to have a good exchange between President Trump and President Putin over what they both see as the nature of this relationship between our two countries".