Before setting off for Moscow, Tillerson told a G7 foreign ministers' meeting in Italy that Russia should rethink its alliance in the light of the latest alleged chemical attack in Syria.
"I think it's also worth thinking about Russia has really aligned itself with the Assad regime, the Iranians, and Hezbollah," he said, referring to Syria's other military allies in its six-year-old civil war.
"Is that a long-term alliance that serves Russia's interest, or would Russia prefer to realign with the United States, with other Western countries and Middle East countries who are seeking to resolve the Syrian crisis?"
When Tillerson's predecessors visited the Russian capital it was usual for them to also be received by President Vladimir Putin, but Russian officials have said that no decision has been made on whether this will be the case.