Sen. John McCain fired back Monday at Donald Trump over his remarks about the Vietnam veteran's time in captivity, saying the presidential candidate doesn't need to apologize to him but owes an apology to the families of those who sacrificed in war. 

The Republican Arizona senator said the best thing to do is "move forward" while also calling Trump's remarks "offensive to veterans." 

McCain weighed in after Trump rocked the Republican presidential primary race with his seemingly offhand but pointed dig at the longtime Arizona senator and former presidential candidate. On Saturday, Trump said McCain, a former Navy fighter pilot who spent five-and-a-half years as a prisoner during the Vietnam War, was a war hero -- but said that's "because he was captured." 

"I like people who weren't captured," he said. 

The comment touched off a firestorm, with Republicans leaping to McCain's defense and suggesting Trump had, this time, gone too far. 

Yet Trump is not backing down. Speaking with NBC's "Today" Show Monday, Trump took issue with the media's reporting on his comments, saying he had said "four times" that he respected those captured in war. 

In an opinion piece published Monday in USA Today, Trump said McCain had abandoned the nation's veterans and made America less secure through his votes in Congress. 

The real estate executive also lashed out at fellow GOP presidential aspirants who have criticized his remarks, calling them "failed politicians." Trump said he did not need "to be lectured by any of them." 

"The reality is that John McCain the politician has made America less safe, sent our brave soldiers into wrong-headed foreign adventures, covered up for President (Barack) Obama with the VA scandal and has spent most of his time in the Senate pushing amnesty," Trump wrote. "He would rather protect the Iraqi border than Arizona's." 

McCain, speaking Monday with MSNBC, said it was "totally inappropriate for Mr. Trump to say he doesn't like to be with people who are captured." 

"I think the point here is that there are so many men and women who served and sacrificed -- and happened to be held prisoner -- and to denigrate in any way that service, I think, is offensive to veterans." 

"The best thing to do is put it behind us and move forward," McCain said. 

Most of the 14 other GOP candidates have condemned Trump's remarks about McCain. 

"This is not just an insult to John McCain, who clearly is a war hero and a great man," Florida Sen. Marco Rubio said on CNN's "State of the Union." "But it's an insult to all POWs, to all men and women who have served us in uniform, who have been captured in battle. ... It's ridiculous. And I do think it is a disqualifier as commander in chief." 

Within hours of Trump's "war hero" comments, former Texas Gov. Rick Perry called for him to drop out, and he repeated his position Sunday. 

Trump on Sunday declined to apologize. 

"Republican candidates, some of whom are registering one percent and zero, they're very upset that I'm leading the polls by actually a nice margin," Trump, a self-funded, billionaire real estate mogul, told ABC's "This Week." "They started attacking me." 

The Associated Press contributed to this report.