Two senior Republican lawmakers on Sunday said they would vote to approve President Donald Trump's nominee for secretary of state, Rex Tillerson, despite their concerns over the former ExxonMobil chief's relationship with Russia's president.

"After careful consideration, and much discussion with Mr. Tillerson, we have decided to support his nomination to be secretary of state," Sens. John McCain of Arizona and Lindsey Graham of South Carolina said in a statement.

"Though we still have concerns about his past dealings with the Russian government and President Vladimir Putin, we believe that Mr. Tillerson can be an effective advocate for U.S. interests," the two senators, who are both regarded as veteran foreign policy experts in the Senate, said in their statement.