"I didn't like the outcome of the 2008 election. But I had a duty to concede, and I did so without reluctance," McCain said in a lengthy statement Thursday. "A concession isn't just an exercise in graciousness. It is an act of respect for the will of the American people, a respect that is every American leader's first responsibility."
The Arizona senator lost to now-President Barack Obama by 7 percentage points eight years ago, about the margin Trump currently trails Hillary Clinton in polls with less than three weeks until Election Day.
But in the third presidential debate on Wednesday night, Trump would not commit to exiting the presidential election quietly, promising that he would leave the country "in suspense."
"I don't know who's going to win the presidential election. I do know that in every previous election, the loser congratulates the winner and calls them, 'my president,' " McCain said. "That's not just the Republican way or the Democratic way. It's the American way. This election must not be any different."
McCain, who is up for reelection this year, originally endorsed Trump despite his disparaging remarks about the Arizona senator. But McCain revoked his blessing in the wake of questions about Trump's treatment of women.
Republicans largely tread carefully around the latest Trump comments. As of mid-day, neither House speaker Paul Ryan or Senate Majority Leader Mitch McConnell had weighed in.
Two Republican critics in the Senate, however, did.
"The American electoral process is the cornerstone of our democracy. Suggesting otherwise undermines an electoral system that is a model for nations around the world," said John Thune, the no. 3 Republican in the body.
"The voters are going to decide this election, and Donald Trump needs to accept the outcome," said Kelly Ayotte, who is in one of the country's tightest Senate races in New Hampshire. If there are reports that need to be investigated, they will be, as I used to do as Attorney General."