Secretary of state says Moscow has responsibility to end conflict, ensure stability
His comments came ahead of President Donald Trump’s first face-to-face meeting with Russian President Vladimir Putin at the upcoming G20 summit in Hamburg, Germany.
"First, parties in Syria must ensure stability on the ground," Tillerson said in a State Department statement.
"Secondly, parties must work through a political process to achieve a settlement that charts a way forward for the Syrian people. Lastly, Russia has a special responsibility to assist in these efforts."
Russia, along with Iran, is the main backer of Bashar al-Assad's regime in the six-year conflict, which has seen more than 400,000 people killed according to the UN special envoy for Syria.
Tillerson said Washington and Moscow had "unresolved" differences on several issues but "have the potential to appropriately coordinate in Syria in order to produce stability and serve our mutual security interests".
He added that Russia had an "obligation to prevent any further use of chemical weapons of any kind by the Assad regime".
Last week, the Organization for the Prohibition of Chemical Weapons found sarin gas was used in the April 4 attack on Khan Sheikhun in opposition-controlled Idlib province. Assad's forces have been widely held responsible for the attack.
Russia and the U.S. had succeeded in establishing "de-confliction zones" to prevent their forces attacking one another, Tillerson said, which showed "that our two nations are capable of further progress".
He added: "The U.S is prepared to explore the possibility of establishing with Russia joint mechanisms for ensuring stability, including no-fly zones, on-the-ground cease-fire observers and coordinated delivery of humanitarian assistance."
Tillerson said stability in Syria would prevent Daesh from "rising anew from the ashes of their failed and fraudulent caliphate".