Hillary Clinton has defended the bereaved parents of a Muslim US army captain, saying Donald Trump displayed a "total misunderstanding" of American values in his criticism of the couple and had inflamed divisions in society.
The Democratic presidential hopeful's comments came after the Republican nominee refused to back down from his response to the Khan family's remarks.
Making her most extensive statement about the Khans since Mr Trump criticised their Democratic National Convention appearance, Mrs Clinton said the Republican nominee had repaid a family who had made the "ultimate sacrifice" with "nothing but insults" and "degrading comments about Muslims".
Mrs Clinton told parishioners at a Cleveland church: "I do tremble before those who would scapegoat other Americans, who would insult people because of their religion, their ethnicity, their disability.
"That's just not how I was raised."
Mr Trump complained on Twitter that he had been "viciously attacked" by Capt Humayun Khan's father, Khizer, during his speech at the convention.
"Am I not allowed to respond?" Mr Trump tweeted. "Hillary voted for the Iraq war, not me!"
At last week's Democratic National Convention, Pakistan-born Mr Khan told the story of his son Humayun, who received a Bronze Star and a Purple Heart after he was killed in Iraq in 2004.
Mr Khan questioned whether Donald Trump had ever read the US Constitution, and told him: "You have sacrificed nothing."
During the speech, Mr Khan's wife, Ghazala, stood quietly by his side.
Mr Trump said in a TV interview: "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."
Ghazala Khan responded in an opinion piece for the Washington Post, in which she revealed that 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.
She wrote: "When Donald Trump is talking about Islam, he is ignorant.
"If he studied the real Islam and Koran, all the ideas he gets from terrorists would change, because terrorism is a different religion."
Her husband told television talk shows on Sunday that he appreciated Mr Trump's later comments that his son was a hero, but said the billionaire had no "moral compass".
At one point, Mr Trump had disputed Mr Khan's criticism that the billionaire businessman has "sacrificed nothing and no-one" for his country.
"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," Mr Trump said.
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, even as calls mounted for them to denounce their party nominee.
John Kasich, the Ohio governor who sought the Republican presidential nomination, said on Twitter: "There's only one way to talk about Gold Star parents: with honour and respect. Capt Khan is a hero. Together, we should pray for his family."
Mr Trump released a statement on Saturday night which called Humayun Khan "a hero", but disputed his father's remarks.
"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 Mr Trump.
The rebuke was unusual 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 over the war, then-president George W Bush responded by saying that the nation grieves every death.
When asked about the mother of a State Department official killed in Benghazi, Libya, who blamed Hillary Clinton for her son's death, Mrs Clinton said her "heart goes out" to the families and that she did not "hold any ill-feeling for someone" who has lost a child and recalls events differently.
Mrs Clinton used her first television interview since officially clinching the Democratic nomination to cast Donald Trump as dangerously pro-Russia and an unknown quantity for US voters.
She said she realises that people often see a "caricature" of herself as a politician, but that she hopes American voters will review her track record as a US senator and secretary of state.
Of her Republican rival, Mrs Clinton said: "He's not temperamentally fit to be president and commander in chief."