Washington (CNN) As Sen. Marco Rubio faces attacks from his own party on his abortion stance, he is seeking to cast Democrats as extremists on the topic -- saying Hillary Clinton would allow abortions until a baby's due date.

"Hillary Clinton is an extremist on this issue," the Florida Republican said Thursday in New Hampshire. "She believes there should be no such thing as an illegal abortion -- even on the due date."

Rubio had been asked about his position on abortion after facing fire on the issue from his own party -- accusing him of being too extreme on the topic.

He said he would not "apologize" for being anti-abortion, though he recognizes the complexity of the issue. And then he pivoted straight to Democrats and Clinton.

"And she believes that partial birth abortion should be legal, which is a gruesome procedure that the vast majority of Americans find to be unconscionable," Rubio said.

It's a line of attack Rubio has used on the trail repeatedly when asked about his abortion policy, arguing that Democrats don't face enough scrutiny of their positions.

Clinton's campaign did not immediately respond to a request for comment.

Rubio himself believes only in exceptions to abortion bans only for the life of the mother, and not for cases of rape or incest. He has indicated, though, that as President he would sign legislation banning abortion if it had broader exceptions.

That stance came under fire Thursday from Rubio's opponent New Jersey Gov. Chris Christie, who said New Hampshire voters should be "really concerned" about Rubio's stance on abortion.

"On the issue of pro-life, Marco Rubio is not for an exception for rape, incest or life of the mother. I think that's the kind of position that New Hampshire voters would be really concerned about," Christie said Thursday on MSNBC's "Morning Joe."

"I'm pro-life but I believe that rape, incest and the life of the mother -- as Ronald Reagan did -- should be exceptions to that rule," he added.

Christie and Rubio are vying for the same Republican voters in New Hampshire, as both seek to present a moderate alternative to Donald Trump and Texas Sen. Ted Cruz. The two have been increasing the intensity of their attacks on one another as polls have showed them drawing close to each other in New Hampshire.

Rubio has accused Christie of donating to Planned Parenthood, an abortion provider, in the past, based on a quote in an old interview. Christie has denied doing so.

With a rift developing in the party, an anti-abortion group is calling for a detente.

The conservative anti-abortion group Susan B. Anthony List on Thursday sent a letter to the remaining candidates asking them to not attack Rubio and Cruz for their positions on abortion.

"Let me be clear: An attack on this aspect of these candidates' pro-life positions is an attack on the pro-life movement as a whole," wrote SBA List President Marjorie Dannenfelser.

Rubio vocalized his opposition to exceptions for abortions during the first Fox News debate held in August 2015, pushing back on Fox News host Megyn Kelly's suggestion that he supported them in the cases of rape and incest.

"I have never said that. And I have never advocated that," Rubio said. "What I have advocated is that we pass law in this country that says all human life at every stage of its development is worthy of protection. In fact, I think that law already exists. It is called the Constitution of the United States."

"I believe that every single human being is entitled to the protection of our laws, whether they can vote or not. Whether they can speak or not. Whether they can hire a lawyer or not. Whether they have a birth certificate or not," he added. "And I think future generations will look back at this history of our country and call us barbarians for murdering millions of babies who we never gave them a chance to live."

Rubio elaborated during a subsequent appearance on NBC's "Meet the Press," "Fortunately, the number of abortions in this country that are due to rape are very small, less than 1% of the cases in the world."