"I obviously have seen no evidence of illegal voting," McCain told CNN's Anderson Cooper. "My focus has been on national security, getting Gen. Mattis in as secretary of defense ... doing those issues."
McCain added that he had learned to disregard at least some of the President's newsmaking remarks and focus on the business of governing.
"A long time ago, honestly, I've stopped reacting to everything that the President has stated and try to work on the issues and the people who he is going to surround himself with, who I am very pleased with as far as national security is concerned," he said, speaking on "AC360."
On Tuesday, White House press secretary Sean Spicer confirmed that Trump believes millions of votes were cast illegally in last year's election, but Spicer declined to give evidence for the claim, which has been repeatedly debunked.
Another Republican senator, Lindsey Graham, also blasted Trump for the claim on Tuesday, saying that he must support it with evidence.
"He needs to disclose why he believes that," Graham told CNN.