"His statements about Syria really disturb me. No, (Russian President Vladimir) Putin does not have it right when it comes to Syria," Graham said on Sunday. "I am so worried about the State Department.”

Tillerson said after attending a meeting between US President Donald Trump and Putin on Friday that Moscow may have "got the right approach" and Washington the wrong one to resolving the ongoing conflict in Syria.

Both Russia and the US have been leading military campaigns in Syria. Unlike Washington, however, Moscow only intervened upon a request from Damascus and has coordinated its airstrikes with Syrian military forces to minimize civilian casualties.

“Maybe they've got the right approach and we've got the wrong approach,” Tillerson said after Putin and Trump’s first meeting on the sidelines of this year’s G20 summit in Hamburg Germany, where the two leaders also agreed on a ceasefire deal in southwest Syria.

In a firm rebuke to Tillerson, McCain, who chairs the Senate Armed Services Committee, said he “sometimes” regretted his support for the former oil-tycoon’s nomination for the job.

“I know that the Russians knew that [Syrian President] Bashar Assad was going to use chemical weapons. And to say that maybe we've got the wrong approach?" he said, referring to an unsubstantiated White House claim that the Assad government has been using chemical weapons against Syrian people.