ATLANTA — With Newt Gingrich campaigning in Georgia on Friday to defend his home turf from competition that has suddenly heated up, a lawyer for his campaign threatened to sue Georgia television stations that run attack ads from a pro-Mitt Romney “super PAC” that connect Mr. Gingrich to Nancy Pelosi and China’s one-child policy.

In a cease-and-desist letter, the lawyer refers to ads run by the super PAC, Restore Our Future, that assert Mr. Gingrich “co-sponsored a bill with Nancy Pelosi that would have given $60 million a year to a U.N. program supporting China’s brutal one-child policy.’’

The lawyer, Patrick Millsaps, writes that the fact-checking site PolitFact found that statement to be a “pants on fire” falsehood, and he warned television stations that if they continue to run the ad “after your receipt of this letter, it will be a knowing publication of a false statement.”

He threatened “potential civil liability.’”

The letter was posted on Mr. Gingrich’s campaign Web site, but Mr. Millsaps did not immediately respond to a question about whether he had sent it to any stations. The bar for winning a defamation or libel judgment against a public figure like Mr. Gingrich is very high, and the letter may simply be intended to call attention to the Gingrich campaign’s charge that it has been wronged.

Earlier in the campaign, a pro-Gingrich super PAC ran ads criticizing Mr. Romney’s record as a corporate takeover specialist at Bain Capital, which fact-checking sites found to be egregiously false. The Romney campaign did not threaten lawsuits.

According to Kantar Media, which monitors political advertising, three versions of anti-Gingrich ads by Restore Our Future mention the one-child policy. They have run in primary and caucus states since Iowa. The newest ad, called “Risk,” appeared on 10 television stations in Georgia on Wednesday and Thursday.

The ads refer to a bill introduced in the House in 1989 called the Global Warming Prevention Act, according to PolitiFact. It would have required the administration to develop plans to reduce carbon emissions and included support for the United Nations Population Fund, although the bill specifically prohibited funding for “the performance of involuntary sterilization or abortion or to coerce any person to accept family planning.’’

Mr. Gingrich and Ms. Pelosi, a Democrat, were co-sponsors of the bill, along with 142 other House members. The bill never became law.