"I told him we miss him," the Majority Leader said.
"I said I was confident I was speaking for everybody in the Senate, and conveying our deepest respects for him and all he's done for the county in his extraordinary life."
McConnell's description of McCain as an "American hero" was picked up by others GOP Senators on Tuesday.
"I'm going to put an exclamation point on that," said Sen. David Perdue (R-GA). "John McCain is an American hero."
GOP Senators have stepped to McCain's defense in the wake of leaked remarks by a special assistant to the President, Kelly Sadler, who had dismissed McCain's opposition to the President's pick for CIA chief by saying McCain's stance didn't matter - "He's dying anyway."
"I regret that comment by that employee, that certainly does not speak for this President or any of us in this caucus," Perdue told reporters.
Sadler reportedly told McCain's daughter that she would publicly apologize, but that has not occurred, and it clearly has been noted on Capitol Hill.
"I think long term in the history of this country, when we think of duty, honor, and country, we will also think of John McCain," said Sen. Mike Rounds (R-SD), who was not asked about McCain, but made sure to tell reporters his views on Tuesday.
At Monday's White House briefing, Deputy Press Secretary Raj Shah said Sadler had apologized directly to the family, as he was pressed several times over why that apology had not been a public one.
"I don't have anything further to add," Shah said.