More Republicans in the U.S. Senate stepped to the defense of ailing Sen. John McCain (R-AZ) on Tuesday, amplifying calls for the White House to publicly apologize over the comments of a top aide to President Donald Trump, who dismissed McCain's opposition to Mr. Trump's CIA nominee, by saying of McCain, "He's dying anyway."

"The person who said that should apologize, and should apologize publicly," said Senate Majority Leader Mitch McConnell after a GOP lunch meeting with the President - but the subject of McCain reportedly did not come up.

"Of course there should be an apology," said Sen. Dan Sullivan (R-AK) during a U.S. Capitol news conference, as he said there should also be more public praise for the 81 year old McCain, who is battling brain cancer.

"I think more broadly, we need to be thinking less about senseless comments, and more about prayers for a great American," Sullivan added.

On Monday, the Majority Leader used a speech on the Senate floor to pay tribute to McCain, as McConnell said he had traveled to Arizona to see their GOP colleague, who has been at home for cancer treatment since December.

"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.