"I have no reaction to 30-year-old gossip when I have Hillary Clinton promising to open the American borders to 600 million people," Gingrich told CNN.
"I don't think it's relevant to the choice of the next president, as compared to Hillary Clinton and her anti-Catholic staff that we're learning about through WikiLeaks," he added.
Gingrich was referring to an exchange in hacked emails released by WikiLeaks that show a Clinton spokeswoman making a critical remark about Catholics.
The New York Times on Wednesday reported on explosive new allegations
in which two women publicly accused Trump of groping them. One of the incidents allegedly took place in the 1980s.
Trump has vehemently denied the allegations and is threatening to sue the Times. People magazine has also published a reporter's claim that she was physically attacked by Trump in 2005.
Gingrich told CNN he has spoken to Trump about how he should handle the recent allegations made against him, saying Trump should focus on immigration and contrast his positions with Clinton. However, he said he "does not know yet" if the GOP nominee has taken his advice.
The former House speaker also said Thursday that, if elected, Clinton would appoint "anti-religious bigots to the Supreme Court."
"The truth is, on the American left, the one bigotry that is acceptable is against Christians," Gingrich said on Fox News. "There's a whole bias here, which also tells you what Hillary Clinton's Supreme Court justices will be like. These are anti-religious bigots who are determined to impose left-wing values using the power of the government."
"If she picks three or four justices, she will permanently move us to the left," Gingrich said.
Gingrich's remarks come as the latest batch of hacked emails from WikiLeaks show Clinton's communications director Jennifer Palmieri making off-color remarks about Catholic Republicans during a correspondence with Center for American Progress senior fellow John Halpin.
In the email, Halpin writes that 21st Century Fox Chairman Rupert Murdoch and NewsCorp Chairman Robert Thomson, who are both Catholic, are attracted to the faith because of "systemic thought and severely backward gender relations."
Palmieri responded: "I imagine they think it is the most socially acceptable, politically conservative religion -- their rich friends wouldn't understand if they became evangelical."
The Trump campaign has denounced the comments and has called on Clinton to fire those involved in the emails.
Palmieri, Halpin and campaign chairman John Podesta, whose emails were hacked, are all Catholic.