"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."
In 2013, Putin awarded the former ExxonMobil CEO the Order of Friendship, one of the highest honors Russia gives to foreign citizens.
The honor has raised concerns that Tillerson is too close to Russia, a country many lawmakers consider one of America's biggest enemies.
Florida Sen. Marco Rubio said last week he was discouraged that Tillerson said he needed more information about Putin before blaming him for questionable acts, including alleged murders of political opponents and critical journalists.
"Is Vladimir Putin a war criminal?" Rubio asked at Tillerson's hearing.
"I would not use that term," Tillerson replied.
While McCain was often critical of President Barack Obama's foreign policy -- including on Russia, he said Tuesday that Americans can be proud that they elected the current president.
"He was a statement to the world that Americans will elect a person as president no matter what their color or creed is," he told Cuomo. "And it was a signal and something that all of us can be very proud of."