He added the US 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 on Wednesday before this week’s Group of 20 summit in Germany.
The statement made no mention of Syrian President Bashar al-Assad‘s future. The US largely blames Assad for the six years of civil war and has called on him to step down.
Tillerson also said Russia had an obligation to prevent the use of chemical weapons by Assad’s government.
Washington hit a Syrian airbase with a missile attack in April after accusing the Assad government of killing dozens of civilians in a chemical attack.
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 of Iraq and the Levant (ISIL, also known as ISIS) and Syrian rebels.
As the fight against ISIL winds down, Tillerson said Russia has a “special responsibility” to ensure Syria’s stability.
He said Moscow needs to make sure no faction in Syria “illegitimately re-takes or occupies areas” liberated from ISIL or other groups.
US-backed forces have surrounded the city of Raqqa, ISIL’s stronghold in Syria.
Tillerson added that Russia has “an obligation to prevent any further use of chemical weapons of any kind by the Assad regime”.
Tillerson lauded US and Russia cooperation in establishing de-confliction zones in Syria and said it was evidence “that our two nations are capable of further progress”.
Speaking to Al Jazeera from the US state of Virginia, Wa’el Alzayat, a former adviser to Samantha Power – the former US ambassador to the UN – said there was no new development coming out of the latest rounds of talks.
“This is really more of the same of what has been tried under the previous administration in terms of dangling the prospect of further cooperation, perhaps against ISIL or now to administer areas after ISIL has been defeated, in exchange of the need for de-escalation and ultimately a sort of a political resolution,” Alzayat said.
“What is not there is the need to have a political transition in Syria … preferably one that includes Assad leaving power,” he said.
Trump came into office in January seeking to improve ties with Russia that had soured during the Obama administration.
But Trump is under pressure at home to take a hard line with Putin due allegations that Russians meddled in the US election and possible collusion between the Trump campaign and Russia.