A Washington Post report, which cited current and former U.S. officials, found that Trump revealed highly classified intelligence about ISIS threats with Russian officials during a meeting in the Oval Office last week.
"We certainly don't want any president to leak classified information, but the president does have the right to do that," McCain said earlier Monday evening, according to the Associated Press.
Republican House Speaker Paul Ryan called for an explanation from the White House.
"We have no way to know what was said, but protecting our nation's secrets is paramount," a spokesperson for Ryan said in a statement. "The speaker hopes for a fully explanation of the facts form the administration."
Tennessee Sen. Bob Corker, a Republican, criticized the White House in comments to reporters on Monday.
"They are in a downward spiral right now and have got to figure out a way to come to grips with all that's happening," Corker said, according to CNN.
Trump Administration officials denied the Post report.
"At no time — at no time — were intelligence sources or methods discussed. And the president did not disclose any military operations that were not already publicly known," National Security Adviser H.R. McMaster said Monday night.
"I was in the room. It didn't happen," he added.