"Being a "friend of Vladimir" is not an attribute I am hoping for from a #SecretaryOfState," Rubio said on his Twitter account.

"It's a matter of concern to me that he has such a close personal relationship with Vladimir Putin and obviously they've done enormous deals together. That would color his approach to Vladimir Putin and the Russian threat," Republican Senator John McCain told CBS.

Among these is Trump's choice for national security adviser, Michael Flynn, who raised eyebrows when he sat beside Russian President Vladimir Putin at a Moscow banquet last year and who has argued that the United States and Russia should collaborate to end Syria's civil war and to defeat Islamic State militants.

Senior senators, both Democrats and Republicans, have expressed concern over Tillerson, who emerged this weekend as Donald Trump's expected pick for secretary of state, according to a source familiar with the situation. By choosing him, the president-elect would add another - and presumably highly influential - person to his Cabinet and circle of advisers who may favor a soft line toward Moscow.

Tillerson, 64, got his start as a production engineer at Exxon in 1975 and has worked there ever since, running business units in Yemen, Thailand and Russia before being named chief executive in 2006. He was expected to retire next year.

The central question facing Exxon Mobil Corp Chief Executive Rex Tillerson if he becomes U.S. secretary of state is whether a lifelong oil man with close ties to Russia can pivot from advancing corporate interests to serving the national interest.

Many U.S. officials are worried by Russia's increasingly aggressive behavior. It annexed Crimea from Ukraine in 2014, has supported Syrian President Bashar al-Assad in the Syrian civil war and is accused of interfering in U.S. domestic politics.

U.S. intelligence analysts have concluded that Russia intervened in the 2016 election to help Trump defeat Hillary Clinton, and not just to undermine confidence in the U.S. electoral system, a senior U.S.official said.

In his role at Exxon, Tillerson maintained close ties with Putin and opposed U.S. sanctions against Russia for its incursion into Crimea.

Daniel Yergin, author of the Pulitzer Prize-winning "The Prize: the Epic Quest for Oil, Money, and Power," said Russia represented a relatively small portion of Exxon's overall operations and played down its significance.

"It was a business relationship," Yergin said. "The whole Russian thing is so much front and center now so it's inevitable that those questions be asked but, obviously, if you are a major oil company, you want to go to where your resources (are). You have to replace your reserves," he added.

"If he becomes secretary of state, the interests he will pursue will be U.S. interests. This is an Eagle Scout kind of guy. He was president of the Boy Scouts," he said. "He is a straight arrow. If that's his mission, that's what he'll do."

Trump praised Tillerson, saying on his Twitter account on Saturday: "Whether I choose him or not for "State"- Rex Tillerson,the Chairman & CEO of ExxonMobil, is a world class player and dealmaker. Staytuned!"

Reince Priebus, the Republican National Committee chairman who has been tapped to serve as White House chief of Staff, praised Tillerson's relationship with Putin. "... the fact that he actually has a relationship with people like Vladimir Putin and others across the globe is something that ... we shouldn't be embarrassed by it. It's something that I think could be a huge advantage to the United States," Priebus said on ABC This Week.

However, Senator Robert Menendez of New Jersey, a senior Democratic member of the Senate Foreign Relations Committee that would weigh Tillerson's nomination, was unsparing in his criticism of the possible appointment.

"Reports that Rex Tillerson could be nominated to be our nation's top diplomat (are) alarming and absurd," he said."With Rex Tillerson as our secretary of state the Trump administration would be guaranteeing Russia has a willing accomplice in the president's cabinet guiding our nation's foreign policy."

Republicans will hold more seats, 52, in the Senate than the 51 they will need to confirm Tillerson. But they will have only 10 of the 19 seats in the Foreign Relations Committee, so it will only take one Republican dissenter there to endanger the nomination.

At least one Republican committee member, Rubio, has already expressed reservations.