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Following a debate where GOP presidential candidate Fred Thompson gave a lackluster performance, the former Tennessee senator is challenging his opponents to meet him for a more personal follow-up — on his terms.

Thompson told FOX News moments after the Republican debate in St. Petersburg, Fla., ended Wednesday night that he next wants to challenge select opponents in a low-key, small-group setting.

"I would like for each of us in small groups ... to sit in small groups and have a discussion, a round-table discussion," Thompson said. "Anybody who's a serious contender for the nomination — I would get to decide as to who I'd get to sit down with, and it'd be several. And I'd do it one-on-one, one-on-three or whatever."

Thompson's comments came after a debate where Republican candidates fielded video questions submitted by viewers on topics ranging from gun control to illegal immigration to the Confederate flag. Some candidates complained afterward of the derisive tone to some of the video submissions.

But Thompson was overshadowed by his rivals over the course of the tense and sometimes-caustic debate.

While Ariz. Sen. John McCain aggressively went after Texas Rep. Ron Paul for his anti-war stances and former New York Mayor Rudy Giuliani sparred with former Massachusetts Gov. Mitt Romney over illegal immigration, Thompson struggled to jump in the fray.

Asked by moderator Anderson Cooper to explain his recent campaign ad where he criticizes Romney for his past support of abortion rights and former Arkansas Gov. Mike Huckabee for his support of tax increases, Thompson hesitated.

Then he quipped, "I just wanted to give my buddies here a little extra airtime."

Thompson got one of his strongest audience responses, though, when he said he would not grant amnesty to illegal immigrants.

"A nation that cannot and will not defend its own borders will not forever remain a sovereign nation. And it's unfair," he said, to loud applause.

He also stirred the crowd after attacking Giuliani for his support of gun control laws, criticism he's tried to emphasize on the trail.

"The Second Amendment is not a choice thing. I mean, it's in the Constitution of the United States," he said. "That's the protection that the people have against."

The former "Law & Order" actor's popularity has steadily fallen in national polls since formalizing his bid in September.

FOX News' Carl Cameron contributed to this report.