He added the United States wanted to discuss with Russia the use of on-the-ground ceasefire observers and the coordinated delivery of humanitarian aid to Syrians.
"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," Tillerson said in a statement ahead of this week's Group of 20 summit in Germany.
Tillerson also said Russia had an obligation to prevent the use of chemical weapons by the government of Syrian President Bashar al-Assad.
U.S. President Donald Trump and Russian President Vladimir Putin are expected to meet on the sidelines of the G20 summit in Hamburg this week, and Tillerson said Syria would be a topic of discussion.
Russia is Assad's major ally and Moscow's military support has helped the Syrian government turn the tide in a multi-sided war against Islamic State and Syrian rebels.
Washington hit a Syrian air base with a missile strike in April after accusing the Assad government of killing dozens of civilians in a chemical attack.