Haley spars with Republican rivals at 3rd primary debate as Trump still looms

While five of his primary challengers were on stage in Miami debating each other and sometimes pointedly attacking him, Trump was rallying supporters in nearby Hialeah, Florida, a heavily Hispanic community.

The former president's remarks tied his familiar attacks on his legal troubles -- he denies all wrongdoing and has pleaded not guilty in four criminal cases -- to the language of being persecuted like in "communist Cuba," in what appeared to be a push to galvanize the local audience.

“We have some great Cubans here,” he said.

He also repeated his recent campaign rhetoric about keeping America and the world safe and peaceful, insisting that under his watch, attacks against Israel and the Russia-Ukraine war would not have happened.

Of the debate, he said, “Nobody's talking about it. Everybody's watching this.”

Hialeah Mayor Esteban Bovo was also invited on stage by Trump where Bovo announced he will ask the City Council to authorize a street named after Trump.

-ABC News’ Lalee Ibssa and Soo Rin Kim

After the debate, the South Carolina senator was seen taking a photo with a blonde-haired woman. The two were physically affectionate, including with their hands interlocked -- and Scott, later asked by a reporter who it was, said, "Oh, my girlfriend."

Scott had said in September that he was dating someone -- "a smart, Christian woman" -- while declining to bring her on the trail, saying that he would introduce her "at some point."

"I have been very protective of my family and my loved ones," he told The Washington Post in September. "I signed up for this. If we make it, she will be signing up for it as well, but at least then she'll know what she's getting into."

-ABC News' Gabriella Abdul-Hakim, Libby Cathey and Fritz Farrow

Ramaswamy, amid a abortion debate, again brought up his idea about "sexual responsibility for men."

"We talked about access to contraception, adoption. Here's the missing ingredient in this movement: sexual responsibility for men," he said. "We live in an era of reliable genetic paternity tests that are 100% reliable, so we can say men deserve more responsibility, so we can tell women, 'We're all in this together.'"

Ramaswamy has discussed this on the trail before but it's not entirely clear what he means or how it would be carried out. He's said it should be codified into law that men have greater responsibility, financially or otherwise, when they are confirmed via paternity test to be a father.

"It's not men's rights versus women's rights," Ramaswamy said on stage. "It's about human rights."

-ABC News' Alexandra Hutzler

Near the end of the night, the candidates were asked to address the path forward for Republicans on abortion restrictions in light of Democrats' successes Tuesday night, which included Ohio voters adding abortion rights to their state constitution.

"I understand that some of these states are doing it a little bit different. Texas is not going to do it the same as New Hampshire. Iowa is not necessarily going to do it the same as Virginia. So you've got to work from the bottom up," DeSantis said.

Haley said they need to find "consensus" and "don't need to divide America over this issue anymore."

"Let's agree on how we can ban late-term abortions. Let's make sure we encourage adoptions. Let's make sure we make contraception accessible. Let's make sure none of these state laws put a woman in jail or give her the death penalty for getting an abortion," she said.

Scott reiterated his call for a "15-week federal limit" and promoted adoption.

Asked whether she would support such a ban, Haley said she would "support anything that would pass," but said the Senate doesn't have the votes.

Ramaswamy did not say whether he would support a 15-week ban when asked. In addition to access to contraception and adoption, he said the "missing ingredient" is "sexual responsibility for men."

Christie said the issue should be left up to the states but said the "bigger issue" was supporting people through challenges post-birth, such as tackling drug addiction.

"Pro-life is not just in the womb," he said. "It's for the whole life."