McCain avoided directly criticising Trump for using Twitter to spread unverified information, but the senator said a serious charge, such as accusing a former President of illegal wiretapping, should not be handled lightly.
"If the allegation is left out there, it undermines the confidence the American people have in the entire way that the Government does business," McCain said.
Several lawmakers, including McCain and Senate Rules Committee chairman Roy Blunt have pointed out that Trump could directly ask intelligence officials to corroborate his claim but instead has asked Congress to investigate.
"The President actually could himself ask that question," Blunt said on Fox News' Sunday Morning Futures.
Not all Republicans have been so quick to put the burden of proof on Trump. Arkansas Senator Tom Cotton agreed with Trump that Congress should take control of the investigation to safeguard sensitive intelligence.
"President Trump said last weekend that he wanted the intelligence committees in the Senate and the House to take up this matter as part of a broader inquiry into Russia's activities in our political system last year. We're going to do that," Cotton today said on ABC's This Week.
"Through a deliberate and careful process of examining all the intelligence at issue here, and then determining with the executive branch what we can declassify, I think the intelligence committees are in the best position to make those decisions," the senator added.