Senator John McCain and other Republican leaders have condemned Donald Trump's remarks about the family of a US Muslim soldier killed in Iraq.
Mr McCain said Mr Trump did not have an "unfettered licence to defame those who are the best among us".
Democratic lawmakers and the soldier's father have called on Republicans to disavow Mr Trump.
US Army Capt Humayun Khan was killed by a car bomb in 2004 in Iraq at the age of 27.
His father, Pakistani-born Khizr Khan, told the BBC on Monday that Mr Trump could not insult women, judges and even members of his own party and not expect to face criticism.
"We all have same equal rights," Mr Khan said.
Mr McCain, a war veteran and the party's 2008 presidential nominee, thanked the Khan family for immigrating to America, adding "we're a better country because of you."
"I cannot emphasize enough how deeply I disagree with Mr. Trump's statement," Mr McCain said in a statement.
"I hope Americans understand that the remarks do not represent the views of our Republican Party, its officers, or candidates."
Last year Mr Trump sparked a backlash after he said Mr McCain was not a war hero because he was captured in Vietnam.
The latest escalation comes as Republican leaders have stepped forward to rebuke Mr Trump's fight against the Gold Star parents.
In the US, parents who have lost a child in war are known as Gold Star families.
Analysis: Jon Sopel, BBC North America Editor
There is a quiet intensity to Mr and Mrs Khan. And an old fashioned courtesy.
But can have anything prepared them for the storm they have whipped up as a result of the intervention at the Democratic convention in Philadelphia and the subsequent round of interviews?
When I met them this morning at our Washington Bureau they seemed weary - and yes emotional too - from their more than fifteen minutes of fame.
But do they have regrets about being catapulted into the limelight?
Not a bit of it.
Khizr Khan says there comes a point in your life where you either stand up and be counted, or you shy away.
But if it's moral support they need they don't have to go far.
Walking them to their car after the interview every passer-by that we met stopped them, thanked them and said they would pray for them - and thanked their son for his service and sacrifice.
It was deeply moving.
Mr Khan and his wife, Ghazala, appeared at the Democratic National Convention in Philadelphia last week to speak about their son's sacrifice.
In an emotional speech, Mr Khan said his son would not even have been in America if it had been up to Mr Trump, who has called for a ban on Muslims entering the US.
In an interview with ABC's This Week, Mr Trump suggested Mrs Khan may have not been allowed to speak.
"She had nothing to say... Maybe she wasn't allowed to have anything to say. You tell me."
Reaction to Mr Trump's comments
- US President Barack Obama made an implicit dig at Mr Trump, saying: "No one has given more for our freedom and our security than our Gold Star families."
- South Carolina Senator Lindsey Graham, Mr Trump's former primary opponent, said: "'Unacceptable' doesn't even begin to describe it."
- House Speaker Paul Ryan condemned any criticism of Muslim Americans who serve their country, but avoided mentioning Mr Trump.
- Ohio Governor John Kasich tweeted: "There's only one way to talk about Gold Star parents: with honour and respect."
- Former Florida Governor Jeb Bush called Trump's remarks "incredibly disrespectful."
- Veterans of Foreign Wars President Brian Duffy: "Election year or not, the VFW will not tolerate anyone berating a Gold Star family member"
- Alabama Senator Jeff Sessions, a Trump supporter, defended Mr Trump's remarks, telling CNN: "His interview was not unkind. It was respectful. It did express condolences to the family for their loss."
Mrs Khan fired back in an opinion article for the Washington Post, saying she was too upset to speak at the convention.
She said Mr Trump was ignorant about Islam and did not know the meaning of the word sacrifice.
Mrs Khan also told the BBC she did not have to speak in order for the audience to understand her pain.
"Without saying a word I was sitting in their heart," she said. "So I was surprised that he doesn't feel the pain."
On Monday, relatives of 11 service members killed in action wrote to Mr Trump, expressing dismay at his treatment of the family of Humayun Khan, and demanding an apology.
"When you question a mother's pain, by implying that her religion, not her grief, kept her from addressing an arena of people, you are attacking us. When you say your job building buildings is akin to our sacrifice, you are attacking our sacrifice," their letter said.
"This goes beyond politics. It is about a sense of decency. That kind decency you mock as 'political correctness'," it went on to say.
Mr Trump's running mate, Governor Mike Pence, released a statement on Sunday avoiding the crossfire and saying he and Mr Trump both believed Capt Khan was an American hero.
Mr Trump's former campaign manager Corey Lewandowski also defended his former boss, saying Capt Khan would still be alive if the billionaire was president "because he would've never engaged in a war that didn't directly benefit this country".
Democratic presidential candidate Hillary Clinton attacked Trump's treatment of the Khans during a campaign stop at a church in Cleveland, Ohio.
"Mr Khan paid the ultimate sacrifice in his family, didn't he?" she told the African American congregation.
"And what has he heard from Donald Trump? Nothing but insults, degrading comments about Muslims, a total misunderstanding of what made our country great - religious freedom, religious liberty," she said.
How many Muslims are there in the US?
Pew Research Center's 2014 Religious Landscape Study found that 0.9% of US adults identify as Muslims.
A 2011 survey of Muslim Americans, estimated that there were 1.8 million Muslim adults (and 2.75 million Muslims of all ages) in the country. That survey also found that a majority of US Muslims (63%) are immigrants.
Demographic projections estimate that Muslims will make up 2.1% of the US population by the year 2050, surpassing people who identify as Jewish on the basis of religion as the second-largest faith group in the country (not including people who say they have no religion).
A Pew Research Center report estimated that the Muslim share of immigrants granted permanent residency status (green cards) increased from about 5% in 1992 to roughly 10% in 2012, representing about 100,000 immigrants in that year.
Source: Pew Research Center