Republican presidential candidate Donald Trump refuses to apologize for saying that Sen.John McCain is "not a war hero." (Reuters)

Sen. John McCain (R-Ariz.) called on Republican presidential candidate Donald Trump to apologize to military families Monday during his first public comments since the flamboyant real estate mogul mocked his military record in a campaign event Saturday.

“I think he may 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 said on MSNBC’s “Morning Joe” Monday, stressing that prisoners of war serve honorably. “Somehow to denigrate that in any way, their service, I think is offensive to most of our veterans.”

McCain called Trump’s comments “totally inappropriate” but dismissed questions over whether Trump owes him a personal apology, instead placing the emphasis on other veterans who have been captured during conflict. He added that it was “the great honor of my life to serve in the company of heroes."

Trump, who has risen to the top of the GOP field according to several national polls, ignited a firestorm after he criticized McCain’s leadership and said that he "never liked him as much after that because I don’t like losers.”

“He’s not a war hero,” Trump said in Iowa Saturday, igniting a swift backlash from Democrats and Republicans alike. "He’s a war hero because he was captured. I like people that weren’t captured.”

[Trump belittles McCain’s war service, sparking stern Republican backlash.]

In a contentious press gaggle after the event, Trump doubled down on his comments and told reporters that the former presidential candidate had failed to lead on veterans' issues.

“John McCain talks a lot, but he doesn’t do anything,” Trump said. “I don’t like the job that John McCain is doing in the Senate because he’s not taking care of our veterans. . . . I’m with the veterans all the time. Some of these people wait four or five days just to see a doctor. They sit in a reception room, which is dirty and filthy and disgusting.”

Republican presidential candidate Donald Trump said Sen. John McCain (R-Ariz.), a decorated Vietnam war veteran, was not a war hero because he was captured by the North Vietnamese. (C-SPAN)

Trump's fellow GOP presidential candidates nearly unanimously condemned his comments, including former Texas governor Rick Perry and Florida Sen. Marco Rubio, who said his comments disqualified him from running for the White House.

[What Donald Trump was up to while John McCain was a prisoner of war.]

The Republican National Committee took the unusual step of weighing in on the controversy as well, sharply condemning the reality television personality's comments, saying there is "no place in our party" for such comments.

“Senator McCain is an American hero because he served his country and sacrificed more than most can imagine. Period,” the RNC’s chief strategist and communications director, Sean Spicer, said in a statement. “There is no place in our party or our country for comments that disparage those who have served honorably.”

Asked if he thought Trump should suspend his White House bid, McCain responded that “I think that’s a decision he would have to make.” He did not directly respond to a question about Trump not serving during the Vietnam War.

“For me to look back in anger at anyone is nonproductive. Our country was divided in almost an unprecedented fashion during the Vietnam War and when I came home I was shocked,” he said. “So I’ve worked ever since to try to heal those wounds. I spend time with veterans. I do everything I can to help them.”

“Who are the real heroes? They’re the 55,000 names that are down on the wall engraved in black granite,” McCain said, noting that he occasionally visits the Vietnam memorial. McCain also added that he spent the Fourth of July with veterans who served in Afghanistan. “I can tell you they are just wonderful — better than my generation,” he said.

It remains to be seen how Trump's comments will influence his poll numbers.

"I can assure you, if you talk to our veterans — and I've had a flood of calls from our veterans — they are not happy," McCain said.