Exxon Mobil CEO Rex Tillerson's reputed friendship with Russian President Vladimir Putin is "a completely false narrative" that shouldn't hurt his nomination, according to former Defense Secretary Robert Gates.

"I think it's a mistake to think that because Rex Tillerson successfully did business in Russia that he's best friends with Vladimir Putin," Gates told PBS' Charlie Rose on Thursday. "I think that's just a completely false narrative."

Gates, who served under President Obama and George W. Bush and is now a partner in a consulting firm that advises ExxonMobil, first recommended Tillerson for the Cabinet position after President-elect Trump failed to settle on a secretary of state nominee. The Exxon Mobil consultant argued that his client's history of negotiating international energy deals and his history with the Boy Scouts of America would render him a tough and capable defender of American interests and values.

"He would bring to the position vast knowledge, experience, and success in dealing with dozens of governments and leaders in every corner of the world," Gates said Tuesday.

Tillerson's nomination provoked criticism from some Republicans and many Democrats due to his history of working with Putin, including his acceptance of the Order of Friendship from Putin in 2013.

Sen. Lindsey Graham, R-S.C., laid out a litmus test for Tillerson, and said the State Department nominee would have to acknowledge that Russia conducted cyberattacks against the Democratic Party during the 2016 election and would have to back retaliatory sanctions against Putin.

Tillerson might resist endorsing future sanctions, if Gates' assessment of his policy views is correct. The former defense secretary said that Tillerson had lobbied against energy sanctions not just because they interfered with Exxon Mobil's energy deal with Russia, but also because Tillerson thinks those sanctions were ineffective.

"I haven't had long conversations with Rex about that, but I suspect it was both," Gates said. "I mean, he was looking out for Exxon's interests and it was informed by his view of what works and what doesn't work. But I think, I think that once Rex Tillerson lifts his hand to take the oath of office, his only objective is going to be to do what is in the best interest of the United States."