Washington (CNN) Donald Trump wouldn't apologize Sunday after igniting a political firestorm a day earlier by questioning whether Sen. John McCain -- who spent five years as a prisoner during the Vietnam War -- is a war hero.

Asked by ABC News whether he owes McCain an apology, Trump said: "No, not at all."

"People that fought hard and weren't captured and went through a lot, they get no credit. Nobody even talks about them. They're like forgotten. And I think that's a shame, if you want to know the truth," Trump said Sunday.

"People that were not captured that went in and fought, nobody talks about them. Those are heroes also," he said.

In an interview on Fox News, Trump hit the Arizona senator again, saying McCain has failed to play a positive role in fixing veterans' lagging health care system.

"He's all talk and he's no action," Trump said.

He also compared the criticism he's faced from Republican presidential contenders to the blowback his comments on undocumented immigrants from Mexico.

"I brought illegal immigration to the forefront. I believe now I'm bringing the veterans -- the plight of the veterans -- to the forefront," Trump said.

Trump's comments came Saturday in Iowa. By mid-afternoon, Trump tried to walk back his blunder on Twitter, saying "captured or not, all our soldiers are heroes!"

But his attempt at damage control seemed unlikely to diminish the anger his remarks had caused. They provoked an immediate outcry from his 2016 presidential rivals and the Republican National Committee, which has expressed concern about the impact his controversial remarks on immigration have had on the GOP brand.

For Republicans waiting to pounce on Trump and knock him from his position as the party's leading presidential candidate , the real estate mogul may have handed them an opening.

The controversy began when Trump, speaking at a question-and-answer session at the Family Leadership Summit in Ames, Iowa, commented on McCain, with whom he's recently feuded over illegal immigration.

"He is not a war hero," Trump told pollster Frank Luntz, who was hosting the session.

"He is a war hero," Luntz interjected.

"He is a war hero because he was captured," Trump said, cutting him off. "I like people that weren't captured, OK? I hate to tell you. He is a war hero because he was captured. OK, you can have -- I believe perhaps he is a war hero."

JUST WATCHED Donald Trump in 2008: I like, respect John McCain Replay More Videos ... MUST WATCH Donald Trump in 2008: I like, respect John McCain 01:17

The comments met with a mix of gasps, boos, laughter and some applause from an audience.

McCain, a Naval aviator, was shot down in 1967 over North Vietnam and fractured both arms and legs after being ejected from his aircraft. He was repeatedly tortured during his stay in the notorious "Hanoi Hilton" -- and refused early release when the North Vietnamese learned his father was a Navy admiral -- until he finally returned home in 1973 following the Paris Peace Accords.

The Arizona senator, who has limited mobility in his arms following his war experience, received the Distinguished Flying Cross, a Silver Star and a Purple Heart for his service.

Trump, meanwhile, received several deferments during the war. According to The Smoking Gun, which obtained selective service records for Trump in 2011, he received four student deferments between 1964 and 1968, and later a medical deferment in 1968.

McCain spokesman Brian Rogers told CNN that the senator would have no comment on Trump's statements.

But McCain's daughter, Meghan, tweeted that she was "horrified" and "disgusted" by the remarks.

"I can't believe what I am reading this morning," she said. "There are no words."

2016 GOP hopefuls rip remark

Trump's comments were swiftly condemned on Twitter Saturday afternoon, with multiple Republican 2016 candidates blasting the remarks.

Former Texas Gov. Rick Perry said in emotional comments made to an audience at the summit that if Trump doesn't apologize, he is unfit to be commander-in-chief of the United States.

"To disparage a legitimate American hero like John McCain -- you may disagree with his policies and that's fine. I tell people all the time it's OK to question your government," said Perry, an Air Force veteran. "But don't question the men and women of the military who sacrifice and sometimes pay a huge price for our safety and our freedom and our economics."

"Enough with the slanderous attacks. @SenJohnMcCain and all our veterans - particularly POWs have earned our respect and admiration," he tweeted.

Enough with the slanderous attacks. @SenJohnMcCain and all our veterans - particularly POWs have earned our respect and admiration. — Jeb Bush (@JebBush) July 18, 2015

Louisiana Gov. Bobby Jindal called McCain "a hero" on Twitter.

John McCain is an American hero. I have nothing but respect for his service to our country. — Gov. Bobby Jindal (@BobbyJindal) July 18, 2015

South Carolina Sen. Lindsey Graham, a close friend of McCain's, fired off a series of tweets criticizing Trump and questioning his qualifications to be president in light of the comments.

At the heart of @realDonaldTrump statement is a lack of respect for those who have served - a disqualifying characteristic to be president — Lindsey Graham (@LindseyGrahamSC) July 18, 2015

But while Texas Sen. Ted Cruz -- who has stood out in the 2016 field as a supporter of Trump's controversial remarks on immigration -- defended McCain in a tweet , he notably declined to criticize Trump when asked by reporters to comment on the real estate mogul's remarks. Instead, he blamed the media for trying to turn Republicans against each other.

"You know I recognize that folks in the press love to see Republican-on-Republican violence, and so you want me to say something bad about Donald Trump, or bad about John McCain or bad about anyone else," he said. "I'm not going to do it."

Retired neurosurgeon Dr. Ben Carson was also asked if he defined McCain as a war hero, and said that while he believed the senator has "done some wonderful things," he also stopped short of denouncing Trump.

"It depends on your definition of a war hero. I think he has done some wonderful things, certainly the history is consistent with what we would consider a war hero," Carson said. "So do we take that away from him because some people disagree with him politically? I think that's probably a stupid way to do things."

Mitt Romney, the 2012 presidential candidate, vouched for McCain's heroism and praised veterans on Twitter.

"The difference between @SenJohnMcCain and @realDonaldTrump: Trump shot himself down. McCain and American veterans are true heroes," he tweeted.

The difference between @SenJohnMcCain and @realDonaldTrump: Trump shot himself down. McCain and American veterans are true heroes. — Mitt Romney (@MittRomney) July 18, 2015

But Trump dismissed Romney -- and McCain again -- in a tweet.

"Why would anybody listen to @MittRomney? He lost an election that should have easily been won against Obama. By the way, so did John McCain," he tweeted.

Sean Spicer, the communications director for the Republican National Committee, said in a statement that McCain "is an American hero because he served his country and sacrificed more than most can imagine. Period."

"There is no place in our party or our country for comments that disparage those who have served honorably," Spicer said.

The other side of the aisle

On a campaign stop in Arkansas, Democratic frontrunner Hillary Clinton weighed in.

"There is nothing funny about the hate he is spewing at immigrants and their families and now the insults he has directed at a genuine war hero, Sen. John McCain," Clinton said. "It is shameful and so is the fact that it took so long for most of his fellow Republican candidates to start standing up to him."

Secretary of State John Kerry, a Vietnam War veteran, said McCain is "a hero, a man of grit and guts and character personified. He served and bled and endured unspeakable acts of torture."

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Speaking to reporters after the event in Ames, Trump sought to clarify his comments.

"If a person is captured, they're a hero as far as I'm concerned," Trump said. "But you have to do other things also. I don't like the job John McCain is doing in the Senate. He's not taking care of our veterans."

His campaign also released a statement, in which Trump said McCain has done "little" for U.S. veterans.

"I am not a fan John McCain because he has done so little for our veterans, and he should know better than anybody what the veterans need, especially in regards to the (Department of Veterans Affairs)," Trump said in the statement. "He is yet another all-talk, no-action politician who spends too much time on television and not enough time doing his job and helping the vets. He is also allowing our military to decrease substantially in size and strength, something which should never be allowed to happen."

Joel Arends, chairman of Veterans for a Strong America, in a statement said feuding between McCain and Trump over issues "has nothing to do with Mr. Trump's high regard for the military or veterans as a whole. Mr. Trump is supporter of the U.S. military and of America's veterans. It is well known that when Mr. Trump is attacked by a detractor, he swings back." The group said it was glad Trump clarified his remarks and said McCain is a war hero.

Trump, McCain feud over immigration

This is not the first time Trump has taken a jab at the 2008 Republican nominee this week.

After McCain criticized Trump's visit to Phoenix last weekend, saying he "fired up the crazies" in regard to his controversial comments on illegal immigration, Trump called the Arizona senator a "dummy" on Twitter.

".@SenJohnMcCain should be defeated in the primaries. Graduated last in his class at Annapolis--dummy," he said.

In his campaign's statement on Saturday, Trump again referenced illegal immigration as the main reason for his feud with McCain.

"Furthermore, he was extremely disrespectful to the thousands upon thousands of people, many of whom happen to be his constituents, that came to listen to me speak about illegal immigration in Phoenix last week by calling them 'crazies,'" the statement said. "These were not 'crazies' -- these were great American citizens."

Trump supported McCain's presidential candidacy in 2008. He donated $28,450 to John McCain's Victory Committee, a super PAC, and endorsed him on CNN's "Larry King Live" that year, calling him "a smart guy and I think he's going to be a great president."

During Saturday's Q&A session, Trump claimed he raised $1 million for the Arizona senator. After the event, Trump added on Twitter that McCain "let us down by losing to Barack Obama in his run for President!"