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Washington • Rex Tillerson, the former Exxon Mobil executive with close business ties to Russia, saw his prospects of becoming secretary of state brighten Sunday after gaining the support of two influential Republican senators who had wavered on the nomination.

"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," Sens. John McCain, R-Ariz., and Lindsey Graham, R-S.C., said in a statement.

Many Democrats and Republicans McCain, Graham and Sen. Marco Rubio of Florida have questioned whether Tillerson has too many conflicts of interests to champion U.S. policy abroad, especially in Russia.

As CEO of Exxon Mobil, Tillerson spoke out against U.S. sanctions levied on Moscow after its annexation of Ukraine's Crimean Peninsula in 2014. The penalties cost the energy giant hundreds of millions of dollars.

Further roiling the debate is U.S. intelligence's assessment that Russia meddled in the presidential election to help Donald Trump defeat Democrat Hillary Clinton in the White House race.

McCain and Graham announced their decision before a vote Monday on Tillerson by the Senate Foreign Relations Committee. While McCain and Graham aren't committee members, their signal of support could make it tougher for Rubio to remain a holdout.

Their support also would make it tough for Democrats to peel off enough Republican votes to oppose his nomination. The Senate is divided by 52 Republicans and 48 Democrats; Tillerson's confirmation needs a simple majority.

Graham told CBS' "Face the Nation" that he was convinced to back Tillerson after a private meeting with the nominee. According to Graham, Tillerson told him "When America doesn't lead, other people will, and the vacuum is always filled by bad actors. He said that we have to have a foreign policy that engages the world. We need to lead from the front."

McCain said on ABC's "This Week" that he talked to Tillerson about his views on Russia and his duty heading a major corporation.

"Listen, this wasn't an easy call," said McCain. "But I also believe that, when there's doubt, the president, the incoming president, gets the benefit of the doubt."