Tillerson said the US would also discuss with Moscow joint efforts to implement ceasefires and deliver humanitarian aid.
He said such efforts would help to lay the groundwork for bringing and end to the civil war that has torn Syria apart over the past six years, and has put Russia and the US on opposing sides.
"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.
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.
During his daily call with reporters, Kremlin spokesman Dmitry Peskov declined to comment on Tillerson's remarks. The Ministry of Defense did not immediately respond to CNN's questions.
Pressure on Russia over chemical attacks
Russia and the United States support opposing sides in Syria -- Russia backs Syrian President Bashar al-Assad and also carries out strikes against anti-Assad rebel groups, some of whom are armed and supported by the US to fight ISIS.
While Trump had supported the idea of creating safe zones within Syria, he seemed to stand against no-fly zones during the campaign. Hillary Clinton was a strong advocate of no-fly zones, while Trump claimed they would increase the likelihood of military confrontation with Russia and lead to "World War III."
Tillerson made no mention of Assad's future, but he did say that Russia, as Syria's most powerful ally, "has an obligation to prevent any further use of chemical weapons of any kind by the Assad regime."
The Syrian regime has carried out a number of deadly chemical attacks
in areas besieged by anti-Assad rebel groups.
One of those attacks prompted the Trump administration to carry out the US' first ever strike against Assad's forces in the Syria
, where the country had been solely targeting ISIS and other terrorist groups.
The change in the Trump administration's attitude to no-fly zones comes as Iraqi forces and rebel groups -- with the help of the US-led international coalition -- make significant gains against ISIS in its two most significant strongholds, Mosul in Iraq and Raqqa in Syria.
US-backed rebels this week breached an ancient wall and entered the city proper of Raqqa, ISIS' de facto capital, beginning what is expected to be a fierce and bloody phase of the conflict. Most of the city of Mosul has now been seized from ISIS fighters.