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The Republican presidential candidates hurled rapid-fire accusations at one another on air and on the stump Friday, as the South Carolina primary race heated up.

Mitt Romney kicked off the day by airing a new TV ad in the state defending his record at investment firm Bain Capital against attacks by his GOP opponents. Conservatives over the last several days have rallied to his defense, warning that the infighting is bad for the Republican Party. Buoyed by their comments, the Romney campaign in its ad highlighted major businesses that Bain Capital once supported, including Staples and Sports Authority, and struck back at critics.

"Mitt Romney helped create and ran a company that invested in struggling businesses, started new ones and rebuilt old ones, creating thousands of jobs," the narrator in the ad says. "Those are the facts."

The ad was followed by an unusual back-and-forth between his campaign and the campaign of Newt Gingrich, who along with Rick Perry has been most critical of Romney's Bain record.

Gingrich, in a written statement, called on the so-called "super PAC" supporting his campaign to either edit or pull ads that portrayed Romney as a corporate raider -- he said the ads contained inaccuracies.

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At the same time, Gingrich called on Romney to likewise call on the super PAC supporting him with anti-Gingrich ads to edit or pull its advertising. He said fact-check organizations found "enormous inaccuracies" in both groups' ads.

Romney has said he will not honor the request because the super PACs are outside of his control. A Romney source told Fox News that Gingrich is merely "distracting from the fact that the movie he has been touting for days ... turned out to be full of blatant falsehoods and fabrications."

The debate was hardly limited to Romney and Gingrich. New polls show several candidates in contention to challenge the former Massachusetts governor for the lead in South Carolina, and those candidates have jumped in the fray.

Rick Santorum, among them, on Friday stepped up his criticism of Romney, calling him "bland and boring" in a fundraising email. He said during a campaign appearance that people would find it hard to vote for Romney because he comes across too much like their boss. Santorum argued that he should be the nominee because he is the best person to challenge Obama.

"We must stop Romney in South Carolina," he urged supporters in the email. "We must unite and guarantee a conservative standard bearer in 2012."

The Romney-aligned super PAC called Restore Our Future, which is running $2.3 million in TV ads in South Carolina alone, is taking no chances of allowing a more conservative alternative to Romney to emerge and drag the race well into the spring. The group is also targeting Santorum on fiscal issues with TV ads and direct mail in South Carolina and in Florida.

The commercials assail Santorum's support for pork-barrel -- or earmark -- spending while in Congress and his votes to increase the federal debt limit. Both were common positions among Republicans, but have become flashpoints for conservatives angry about spending and the federal budget deficit.

"So how will Santorum beat Obama? Obama knows he can't," the ad says.

A Rasmussen Reports poll Friday showed Romney leading in South Carolina with 28 percent, followed by Gingrich with 21 percent and Santorum and Paul with 16 percent each.

With the Bain issue now spreading across both the primary and general election campaigns, Romney's campaign has been trying to squelch the attacks -- in part by actively circulating conservative criticism of them.

Examples are not hard to find.

On Thursday, Perry lost a key South Carolina donor to the Romney campaign over his remarks. Ex-Perry supporter Barry Wynn said Perry's attacks were "like fingernails on the chalkboard."

Republican New York Rep. Michael Grimm also released a statement saying the attacks would have a "negative effect on the party."

"When GOP candidates, especially those who identify themselves as conservatives, use phrases like 'vulture capitalism' or adopt leftist rhetoric, they are jeopardizing the strength and unity of the party," he said.

Thomas Donohue, president of the U.S. Chamber of Commerce, said Thursday he was disappointed by the rhetoric.

"It's just been foolish," he said. "They're not doing anything other than setting up the ad base for their (Democratic) opponents."

The condemnations come on top of criticism from conservative mainstays ranging from the Club for Growth to Rush Limbaugh to Americans for Prosperity.

It's unclear whether Gingrich and Perry will back off. Perry continued to lob charges at Romney on Thursday, telling Fox News that in some cases Bain had "come in and basically taken the profits out of these companies, and sold them for a quick profit -- I'm not for that, I don't think most people in South Carolina are."

Under pressure, Gingrich on Thursday tempered his public attacks on Romney while defending his right to question Romney's business record, before calling Friday for the super PAC supporting him to change or pull its ad.

"I think he owes the country a much more detailed answer about what his career was like," he said during a Fox News interview Thursday night of the questions he and his allies have raised about Romney's tenure as head of a private equity fund.

Other GOP candidates, including Paul and Jon Huntsman, have rejected the Romney criticism.

Although Huntsman had criticized Romney for a comment he made about firing people, Huntsman said on Wednesday: "If you have creative destruction in capitalism, which has always been part of capitalism, it becomes a little disingenuous to take on Bain Capital."

The Associated Press contributed to this report.