"Your recent comments regarding the Khan family were repugnant and personally offensive to us," they wrote in a letter to Trump.
The group of 11 "Gold Star" families are those who have lost a family member in war.
"We feel we must speak out and demand you apologise to the Khans, to all Gold Star families, and to all Americans for your offensive, and frankly anti-American comments."
Trump responded by criticising his wife, Ghazala Khan, for her silence during his speech and suggesting she was not allowed to speak.
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The also group rejected the idea that Trump was being unfairly criticised for his remarks out of "political correctness."
"You are not just attacking us, you are cheapening the sacrifice made by those we lost. You are minimising the risk our service members make for all of us. This goes beyond politics. It is about a sense of decency. That kind decency you mock as 'political correctness.'"
Meanwhile, Trump has defended his criticism of the bereaved parents of Humayun Khan by complaining on Twitter that the father "viciously attacked" him in his speech at the Democratic National Convention.
"Am I not allowed to respond?" Trump tweeted. "Hillary voted for the Iraq war, not me!"
Pakistan-born Khizr Khan's son Captain Humayun Khan was killed in Iraq in 2004.