Story highlights McCain said Tuesday he is still learning more about Tillerson

In 2013, Putin awarded the former ExxonMobil CEO the Order of Friendship

Washington (CNN) Sen. John McCain said Tuesday that he has not decided whether he will back Rex Tillerson for secretary of state given existing concerns about his relationship with Russia.

"When I see what Vladimir Putin has done in the way of literally committing war crimes intentionally -- I'm pointing out again precision weapons used in Aleppo to strike hospitals and kill innocent men, women and children, that's just an example -- then I question the recipient of a friendship award with Vladimir Putin," the Arizona Republican told CNN's Chris Cuomo on "New Day."

McCain said he is still learning more about Tillerson.

"I had another conversation with him yesterday where I think he explained better to me his relations with Vladimir Putin."

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