"There's not one shred of truth to it," Thompson told Fox News.
Huckabee, the former Arkansas governor and a Fox News host, had claimed a day earlier that ahead of the 2008 Republican South Carolina primary, McCain had "certainly encouraged" Thompson to stay in the race. At the time, Huckabee had just won the Iowa caucuses and McCain had won the New Hampshire primary -- a win in South Carolina, which McCain ultimately achieved, was considered vital to his campaign.
Huckabee claimed he's been told that McCain urged Thompson to stay in the race and that, in turn, Thompson soaked up some of the votes that would have gone toward the Huckabee campaign.
Huckabee said Friday, in response to Thompson, that he meant his allegation as a compliment, since it would have been a deft political move. "I thought it was a brilliant strategy," he said. "If they weren't smart enough to do it, then I apologize for giving them the benefit of being that smart."
Huckabee said earlier that he doesn't "blame" either of the two candidates for the alleged political play.
"Many people in the McCain camp have since confirmed, you know, that he said please stay in, I need you in South Carolina, primarily in the upstate where I had my strength," Huckabee said. "But you know what, that's politics, that's what happens. It was an honest, a good, a straightforward political move on his part. I had to congratulate him for it, but it was very painful at the time."
However, both McCain and Thompson adamantly deny it.
"Senator McCain and I never had a conversation about staying in the race, being out of the race," Thompson said Friday. "We didn't have a conversation about it. We didn't have a conversation with the intermediaries. ... If you know me, and certainly if you know John, that's not us."
McCain also said the charge is untrue.
"I respect (Huckabee), but that's totally false. It's totally, patently false," McCain told Fox News.
The back-and-forth comes as the 2012 GOP presidential candidates charge into South Carolina. And once again, there is speculation about the possibility that the winner of the New Hampshire primary -- Mitt Romney -- could benefit in South Carolina from social conservatives being divided over the other candidates.