Sen. John McCainJohn Sidney McCainThe Memo: Activists press Biden on VP choice Biden takes page from Trump with public auditions for VP slot Why Trump, GOP are running into trouble in Arizona MORE on Monday played down his personal spat with Donald TrumpDonald John TrumpTrump retweets personal attacks on Clinton, Pelosi, Abrams Biden swipes at Trump: 'Presidency is about a lot more than tweeting from your golf cart' GOP sues California over Newsom's vote-by-mail order MORE, but said that Trump should apologize to prisoners of war after the GOP presidential candidate’s controversial comments mocking McCain for being captured during the Vietnam War.

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"He might owe an apology to the families of those who have sacrificed in conflict and those who have undergone the prison experience in serving their country," McCain (R-Ariz.) said on MSNBC's "Morning Joe," adding that Trump didn't owe him a personal apology.

"Many men and some women who served and sacrificed and happened to be held prisoner. To denigrate that service in any way is offensive to veterans."

The comments come just minutes after Trump refused to back down during an interview with NBC's "Today" show in which Trump bashed McCain's record in Congress on veterans’ issues and immigration. Trump said over the weekend that McCain was not a war hero because he was captured during the war.

McCain had previously drawn the ire of Trump when he referred to those who came to his rally in Arizona as "crazies." He joked to the "Morning Joe" hosts that he's been called a "crazy" by many Arizonans during town hall meetings and that he didn't mean to offend.

"I thought it was a term of endearment," McCain said with a smile. "I meant it as a term of affection, I'll be honest with you."