"You dodged the draft," Khan, a Muslim whose son was slain in the Iraq War, said of Trump to CNN's Anderson Cooper. "Put that Purple Heart back on that person's chest."
A military veteran supporting Trump had gifted the Republican presidential nominee his Purple Heart, prompting Trump to say he "always wanted to get the Purple Heart" and this was "much easier" than serving in combat.
Khan's own son, Capt. Humayun Khan, was also a Purple Heart recipient. It is bestowed upon those wounded or killed in combat.
Khan criticized Trump at last week's Democratic National Convention, spurring Trump to lash out at Khan and his wife over the weekend. Khan and Trump have traded verbal blows in the days since.
"You had the time. You did not serve," Khan told Cooper. "You should have pinned that back to that veteran's chest and should have hugged him and thanked him."
Trump avoided the US military draft during the Vietnam War thanks to four student deferments and one medical deferment after he was diagnosed with bone spurs in his heels, The New York Times reported Monday
"I've regretted not serving in many ways," Trump said Tuesday in an interview with Gray Television after his rally in Ashburn, Virginia. "So many of the greatest people I know have served."
The multi-day imbroglio with Khan has dragged Trump way off-message and invited some Republican leaders to pull the plug and no longer support Trump's candidacy.
Khan continued to sharply criticize Trump, saying that he "does not comprehend what is coming out of his mouth."
Khan said he did not need an apology from Trump, but rather a display of empathy. And he indicated that he was growing tired of pressing his case against the GOP nominee.
"I will continue to remind you what your behavior for a whole year had been," he said. "I am not going to continue to appear on television. It is very disturbing. Because it is emotionally disturbing, it is family-wise disturbing. But I wanted to say this today."