Rudy Giuliani told FOX News on Saturday that GOP rival Fred Thompson has "no record," after Thompson repeatedly took shots at Giuliani for supporting gun control legislation and bringing up his record as mayor of New York City on the campaign trail.

"Fred has no record to talk about ... I have a good record to talk about so I am very proud of it," Giuliani said while campaigning in Nashua, N.H. "If you didn't have a good record you would want to run away from it. And if you had no record at all, you would want to attack somebody else's record, which is what I think some of my opponents are doing. They don't have the record of results that I have so instead ... they attack you."

The accusation came after Thompson chided Giuliani Friday while visiting a New Hampshire gun store.

"(Giuliani) simply supported just about every gun control legislation that came down the pike. And I just disagree with him on that.... over the years and he's been very outspoken about it. Of course he's not outspoken about it anymore," Thompson told reporters with a smile. "It's a major differentiation. He relates everything to New York City ... Well, New York City is not emblematic of the rest of the country.

"And the sentiments of those people in the rest of the country are in support of the second amendment. This is where I've always been ... and I don't think he's ever been," he said.

Thompson repeated his criticism about Giuliani's gun control positions Saturday at the Land and Sky Gun Show in South Carolina.

The former Tennessee senator and "Law & Order" actor consistently ranks in the top tier of presidential candidates in national polls, but his fortunes in New Hampshire, which just set its influential first-in-the-nation primary for Jan. 8, have taken a turn.

Thompson pulled only 4 percent in the latest CNN-WMUR-TV poll of 404 likely Republican voters in the Granite State. The same poll showed Giuliani with 16 percent and former Massachusetts Gov. Mitt Romney with 33 percent support. The poll, taken from Nov. 14-18, had a margin of error of 5 points.

Giuliani, who leads in most national polls, regularly turns voters' attention to his record in New York as mayor during the Sept. 11 attacks, as well as his record as a mob-busting, crime-fighting federal prosecutor. He has justified his support of gun control legislation by saying it helped reduce crime in New York.

In response to Giuliani's comments Saturday, Thompson's campaign released a statement saying the former senator has a "strong record" supporting second-amendment rights and pro-life causes.

FOX News' Cristina Corbin and Mosheh Oinounou contributed to this report.