AP
Donald Trump at a rally in Dallas, Texas.
Trump had responded to a question about whether he thought he was ready to be handed the keys to the country's nuclear codes by slamming Paul, who has been a frequent sparring partner for Trump on the campaign trail.
"First of all, Rand Paul shouldn't even be on the debate stage," Trump said.
"He's No. 11. He's got 1% in the polls. And how he got up here, there's far too many people anyway. And we all know that. As far as temperament, I think I have a great temperament."
Paul responded by saying Trump's attack didn't have anything to do with the matter at hand. And he was one of the only candidates to say he was "concerned" about having Trump in charge of the country's nuclear arsenal because of his penchant to overreact to criticism.
He alluded to Trump's recent mocking of presidential rival Carly Fiorina's appearance.
"I kind of have to laugh, when I think of, 'Hmm, it sounds like a non-sequitur.' He was asked whether or not he would be capable … to be in charge of the nuclear weapons and all of a sudden there's a sideways attack at me. I think that really goes to really the judgment. Do we want someone with that kind of character, with that kind of careless language, to be negotiating with Putin?" Paul said.
He added: "I'm very concerned about having him in charge of the nuclear weapons because I think his visceral response to attack people on their appearance - short, tall, fat, ugly - my goodness, that happened in junior high. Are we not way above that? Would we not all be worried to have someone like that in charge of the nuclear arsenal?"
Trump shot back with a zinger at Paul's looks.
"I never attacked him on his looks and believe me: There is plenty of subject matter right there," Trump said.
That remark prompted Paul to smirk.