Sen. John McCain has joined the growing number of voices condemning Donald Trump for his attack on the family of a Humayun Khan, a slain Muslim American soldier whose parents challenged Trump at the Democratic National Convention last week.

"Captain Khan's death in Iraq, on June 8th, 2004, was a shining example of the valor and bravery inculcated into our military," McCain said in a statement on Monday. He also thanked Khan's father, Khizr, and mother Ghazala for immigrating to the United States, saying: "We're a better country because of you."

Capt. Humayun Khan was killed by a suicide bomber in Iraq in 2004. Last week, his father Khizr Khan challenged Trump's anti-Muslim platform in an emotional speech at the DNC, where he suggested Trump had "sacrificed nothing" and that he had never even read the United States Constitution. Ghazala Khan stood by his side during the speech, but did not speak. She later said she was too emotional to say anything.

Trump was quick to fire back at the Khans, insisting that he had made many sacrifices to build his business empire. He also suggested Ghazala Khan had been forced into silence. On ABC's "This Week," Trump said: "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."

Ghazala Khan told CNN she was extremely upset by Trump's remarks, and that all of America felt her pain as she stood silently during her husband's speech: "Please Mr. Trump, feel that pain," she said.

Many high-profile Republicans were quick to distance themselves from Trump's attack on a military family. In addition to McCain, House Speaker Paul Ryan and Senate Majority Leader Mitch McConnell also issued statements praising Humayun Khan. However, McCain was the only one of those three individuals to mention Trump by name.

"I claim no moral superiority over Donald Trump," McCain said, adding that Trump should be setting an example for the country and his party. "While our Party has bestowed upon him the nomination, it is not accompanied by unfettered license to defame those who are the best among us," he said.

Republican Sen. Roy Blunt of Missouri also criticized Trump on Monday, saying he should "focus on jobs and national security and stop responding to every criticism, whether it's from a grieving family or Hillary Clinton." Blunt also said the Khans "deserve to be heard and respected."

Republican Sen. Kelly Ayotte, from New Hampshire, also harshly rebuked Trump. "I am appalled that Donald Trump would disparage (the Khans) and that he had the gall to compare his own sacrifices to those of a Gold Star family," she said.

Political reporter Jesse Byrne of "The Hill" says Trump's attack on the Khans is unprecedented, and is going to create a lot of headaches for the GOP leadership. "It's certainly remarkable to have the Republican nominee be publicly feuding with the parents of a slain American soldier," he told CTV News Channel.

Byrne pointed out that while Trump has softened his anti-Muslim stance recently, this situation is likely to put the issue back into the spotlight. "It's going to be something that GOP leaders are going to have to answer for," he said.

Trump said on Twitter Sunday that he was "viciously attacked" by Khizr Khan. "Am I not allowed to respond?" he tweeted. "Hillary voted for the Iraq war, not me!"

Trump's running mate, Indiana Gov. Mike Pence, issued a statement of his own on Sunday night, hailing Capt. Khan as a hero while backing Trump's immigration policy.

With files from The Associated Press