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WASHINGTON — Refusing to back down, Donald Trump on Sunday defended his criticism of the bereaved parents of a Muslim U.S. Army captain by complaining on Twitter that the father “viciously attacked” him in his speech at the Democratic National Convention.

“Am I not allowed to respond?” Trump tweeted. “Hillary voted for the Iraq war, not me!”

I was viciously attacked by Mr. Khan at the Democratic Convention. Am I not allowed to respond? Hillary voted for the Iraq war, not me! — Donald J. Trump (@realDonaldTrump) July 31, 2016

It was the latest bitter rhetorical volley between the defiant Republican candidate and the family of a fallen soldier since the two parties concluded their major conventions last week and the nation looked ahead to a close election this November. Wasting no time, Trump headed to Colorado — a key swing state — while Hillary Clinton took running mate Sen. Tim Kaine on a bus-tour through Ohio and Pennsylvania.

WATCH: ‘I made a lot of sacrifices’: Trump after his patriotism was criticized by Muslim DNC speaker

2:36 ‘I made a lot of sacrifices’: Trump after his patriotism was criticized by Muslim DNC speaker ‘I made a lot of sacrifices’: Trump after his patriotism was criticized by Muslim DNC speaker

At last week’s Democratic National Convention, Pakistan-born Khizr Khan told the story of his son who received a Bronze Star and a Purple Heart after being killed in Iraq in 2004. Khan questioned whether Trump had ever read the Constitution and said “you have sacrificed nothing.

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During the speech, Khan’s wife, Ghazala, stood quietly by his side.

“If you look at his wife, she was standing there. She had nothing to say. She probably, maybe she wasn’t allowed to have anything to say. You tell me,” Trump said, in an interview with ABC’s “This Week.”

There's only one way to talk about Gold Star parents: with honor and respect. Capt. Khan is a hero. Together, we should pray for his family. — John Kasich (@JohnKasich) July 31, 2016

Ghazala Khan responded Sunday in an opinion piece published in the Washington Post, saying talking about her son’s death 12 years ago is still hard for her. When her husband asked if she wanted to speak at the convention, she said she could not.

“When Donald Trump is talking about Islam, he is ignorant,” she wrote. “If he studied the real Islam and Koran, all the ideas he gets from terrorists would change, because terrorism is a different religion.” Tweet This

Her husband told television talk shows on Sunday that he appreciated Trump’s later comments that his son was a hero but that he had no “moral compass.

WATCH: Trump’s apology ‘sounds so disingenuous’ because of his rhetoric: Khizr Khan

1:38 Trump’s apology ‘sounds so disingenuous’ because of his rhetoric: Khizr Khan Trump’s apology ‘sounds so disingenuous’ because of his rhetoric: Khizr Khan

At one point, Trump had disputed Khan’s criticism that the billionaire businessman has “sacrificed nothing and no one” for his country.

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“I’ve made a lot of sacrifices. I work very, very hard. I’ve created thousands and thousands of jobs, tens of thousands of jobs, built great structures,” Trump said. Tweet This

Senior Republican leaders, including House Speaker Paul D. Ryan and Senate Majority Leader Mitch McConnell, remained silent on Sunday, as did vice presidential nominee Mike Pence.

But John Kasich, the Ohio governor who sought the GOP presidential nomination, said on Twitter, “There’s only one way to talk about Gold Star parents: with honor and respect. Capt. Khan is a hero. Together, we should pray for his family.”

Late Saturday night, Trump released a statement calling Humayun Khan “a hero” but disputing his father’s characterization.

READ MORE: Donald Trump rebuts soldier’s dad’s speech: ‘I’ve made a lot of sacrifices’

“While I feel deeply for the loss of his son, Mr. Khan who has never met me, has no right to stand in front of millions of people and claim I have never read the Constitution, (which is false) and say many other inaccurate things,” said Trump.

WATCH: Father of U.S. Muslim soldier killed in Iraq blasts Donald Trump, offers him his copy of U.S. constitution

5:07 Father of U.S. Muslim soldier killed in Iraq blasts Donald Trump, offers him his copy of U.S. constitution Father of U.S. Muslim soldier killed in Iraq blasts Donald Trump, offers him his copy of U.S. constitution

Trump’s rebuke seemed strange in the world of politics where officials only speak well of families whose loved ones die in service to their country. When Cindy Sheehan, who lost her son in Iraq, staged prolonged protests on the war, then-President George W. Bush responded by saying that the nation grieves every death.

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Captain Khan, killed 12 years ago, was a hero, but this is about RADICAL ISLAMIC TERROR and the weakness of our "leaders" to eradicate it! — Donald J. Trump (@realDonaldTrump) July 31, 2016

When asked about the mother of a State Department official killed in Benghazi, Libya, who blamed Hillary Clinton for her son’s death, Clinton told “Fox News Sunday” that her “heart goes out” to the families and that she didn’t “hold any ill feeling for someone” who has lost a child and recalls events differently.

WATCH: Will the conventions boost Clinton, Trump campaigns?

3:02 Will the conventions boost Clinton, Trump campaigns? Will the conventions boost Clinton, Trump campaigns?

Clinton used her first television interview since officially clinching the Democratic nomination to cast Trump as dangerously pro-Russia and an unknown quantity for U.S. voters. She said she realizes that people often see a “caricature” of herself as a politician but that she hopes American voters will review her track record as a U.S. senator and secretary of State.

‘He’s not temperamentally fit to be president and commander in chief,” she said.

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