"You believe he faked a disability?" Costa asked.
"Do you believe he has a disability? Yeah. Yeah. At least not that one," Buttigieg said, targeting the president in jest.
He continued, "I don't mean to trivialize disability, but I think that's exactly what he did.
"This is somebody who, I think it's fairly obvious to most of us, took advantage of the fact that he was a child of a multimillionaire in order to pretend to be disabled, so that somebody could go to war in his place."
Trump was exempted from military service in the 1960s after receiving a letter from a doctor saying he had a bone spur ailment.
"I asked for student deferment, like many other people during the war or around the time of the war. I had a minor medical deferment for feet, for a bone spur of the foot, which was minor," Trump said in an interview with ABC News in July 2015. "I was not a fan of the Vietnam War. But I was entered into the draft, and I got a very, very high draft number."
It's not the first time someone has accused the president of faking his medical problem. The president's former personal attorney, Michael Cohen, made a similar claim in his first public testimony to Congress in February.
"Mr. Trump claimed it was because of a bone spur, but when I asked for medical records, he gave me none and said there was no surgery," said Cohen.
Cohen claimed the president told him, "You think I'm stupid, I wasn't going to Vietnam."