While House Speaker Paul Ryan said a "religious test" for entering the US is "not reflective of the country's fundamental values", former Florida Governor Jeb Bush said the reality TV star's remarks were "disrespectful" in targetting a family that endured the "ultimate sacrifice" for the country.
Ryan hailed Army Capt. Humayun Khan, who was killed by a suicide bomber in Iraq in 2004, and said America's greatness is built on the principles of liberty and preserved by the men and women who wear the uniform to defend it.
"Many Muslim Americans have served valiantly in our military, and made the ultimate sacrifice. Captain Khan was one such brave example. His sacrifice - and that of Khizr and Ghazala Khan - should always be honoured. Period," he said.
Governor John Kasich of Ohio, a former Republican presidential candidate, tweeted: "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."
In an interview to CNN, Senator Jeff Session who was among the first few top Republican leaders to endorse Trump said that he "rejects" and is "disappointed" over the remarks made by the billionaire from New York against Khan.
The 70-year-old real estate tycoon sparked controversy last week when he lashed out at Humayun's father Khizr Khan over his speech on Thursday at the Democratic National Convention in which he was highly critical of Trump and said that the billionaire has "sacrificed nothing" for the country.
Many criticised him both for attacking a mourning mother and because many considered the remarks racist and anti- Muslim, especially because they came from someone who has called for a ban on Muslims entering the US.
"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!" Trump tweeted, even as his running mate came to his rescue giving another set of clarification.
In an op-ed in The Washington Post, Ghazala Khan, mother of Humayun, lashed out at Trump and said that he is ignorant about Islam.
Ghazala said: "When Donald Trump is talking about Islam, he is ignorant. If he studied the real Islam and Quran, all the ideas he gets from terrorists would change, because terrorism is a different religion.
"Donald Trump said he has made a lot of sacrifices. He doesn't know what the word sacrifice means."
In a statement, Senate Minority Leader Harry Reid urged the Senate Majority Leader Mitch McConnell and House Speaker Ryan to revoke their endorsement of Trump.
The Council on American Islamic Relations (CAIR) yesterday demanded that Trump apologises on his comments and is urging Muslim women to speak out against him.
Pence said: "Captain Khan gave his life to defend our country in the global war on terror. Due to the disastrous decisions of Barack Obama and Hillary Clinton, a once stable Middle East has now been overrun by ISIS. This must not stand.
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Senator John McCain also said he disagrees with Trump over the issue.
"Captain Khan's death in Iraq, on June 8th, 2004, was a shining example of the valour and bravery inculcated into our military. When a suicide bomber accelerated his vehicle toward a facility with hundreds of American soldiers, Captain Khan ordered his subordinates away from the danger," he said.
"I claim no moral superiority over Donald Trump. I have a long and well-known public and private record for which I will have to answer at the Final Judgement, and I repose my hope in the promise of mercy and the moderation of age. I challenge the nominee to set the example for what our country can and should represent," McCain said.
Meanwhile, family members of seventeen fallen service-members in a letter to Trump expressed their dismay at his treatment of the family of Capt Humayun and demanded an apology.
