Trump, in an ABC interview that aired on Sunday (local time), questioned why Ghazala Khan, mother of US Army Captain Humayun Khan, stood quietly by her husband, Khizr Khan, as he took the stage at last week's Democratic convention in Philadelphia.
Trump suggested the mother might not have been "allowed" to speak.
Speaking at a church service, Clinton said Trump had been insulting to a family who had sacrificed so much. She also used the episode to contrast her own religious faith with that of Trump, who has spoken of religion on the campaign trail infrequently.
"I don't begrudge anyone of any other faith or of no faith at all, but I do tremble before those who would scapegoat other Americans, who would insult people because of their religion, their ethnicity, their disability," Clinton said in remarks at the Imani Temple Ministries, an African-American church in Cleveland Heights, Ohio.
"It's just not how I was raised, that's not how I was taught in my church," said Clinton, who grew up as a Methodist. "Tim Kaine and I are people of faith," she said, referring to her vice presidential running mate, who is a Catholic.
Earlier on Sunday, Ghazala Khan took up her own defense in an opinion piece in the Washington Post, saying her husband had asked her in advance whether she would want to speak at the convention but she had decided she would be unable to do so on stage because of her pain over the 2004 death of her son.
"Donald Trump said that maybe I wasn't allowed to say anything. That is not true," she wrote. "When Donald Trump is talking about Islam, he is ignorant."
Trump stirred bipartisan outrage for his back and forth with the Khans.
The Republican nominee lashed out at Khizr Khan, a US citizen of Pakistani origin and a Muslim, when Khan told of his war hero son at the convention and took issue with Trump's call for a temporary ban on the entry of Muslims into the United States.
Khizr Khan invited the Republican nominee to read the US Constitution and visit the graves of American soldiers from many backgrounds at Arlington National Cemetery.
In the interview aired on Sunday on ABC's 'This Week', Trump cast doubt on why Khan's wife did not speak.
"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.
Trump on Sunday tweeted that Khan's son had died 12 years ago: "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!"
Trump also tweeted that he had been "viciously attacked" by Khan at the convention. "Am I not allowed to respond?" he asked. The candidate also tried to change the subject to the war itself: "Hillary voted for the Iraq war, not me!"
On Twitter, Republican strategist Ana Navarro called Trump's comments about the Khans "gross" and labeled him a "jerk."
US Senate Majority Leader Mitch McConnell called slain soldier Khan "an American hero" in a statement issued on Sunday and said he agreed with the Khan family than banning people from entering the United States based on their religion was contrary to American values.
Trump's campaign manager, Paul Manafort, said he sympathizes with the Khan family but that their loss is not the issue at hand.
"The issue really is radical Islamic jihad and the risk to the American homeland," he said on CBS, defending Trump's proposal to suspend immigration from some geographic regions.
"He [Khan] is not the issue. We all feel sorry for what he went through," Manafort said.
