Nikki Haley says she'll only debate Trump or Biden, suggesting she ...

After former President Donald Trump dominated the Iowa caucuses, Republican presidential candidate Nikki Haley said in a statement on Tuesday that she will debate only Trump or President Joe Biden.

"We've had five great debates in this campaign," the former South Carolina governor said. "Unfortunately, Donald Trump has ducked all of them. He has nowhere left to hide. The next debate I do will either be with Donald Trump or with Joe Biden. I look forward to it."

Haley's statement came after a third-place showing in Iowa's caucuses where she got 19% of the vote -- behind Florida Gov. Ron DeSantis with 21% and Trump with 51%.

Shortly after Haley's statement, DeSantis fired back, posting on X that Haley "is afraid to debate because she doesn't want to answer the tough questions."

"The reality is that she is not running for the nomination, she's running to be Trump's VP," DeSantis wrote.

ABC and New Hampshire TV station WMUR plan to host the next Republican primary debate, on Thursday in New Hampshire. While DeSantis has publicly said he'll attend, Haley's new statement suggests she doesn't plan to.

"ABC News and WMUR-TV have officially given Donald Trump and Nikki Haley’s campaigns a deadline of 5:00 p.m. EST today to commit to the Republican presidential primary debate planned for Thursday, Jan. 18 at Saint Anselm College in Manchester, New Hampshire," an ABC News spokesperson said in a statement. "We will update our plans accordingly."

Trump has not participated in any of the GOP debates so far, saying he saw no point given his large polling lead.

"President Trump's statement was that he would not attend the debates," adviser Chris LaCivita said after the second GOP debate. "Plural ... And that's his position until it's not."

Instead, Trump has favored counterprogramming events such as rallies or televised interviews.

The South Carolina Republican has seen a consistent bump in polling since September, including recent polls that showed her narrowly ahead of DeSantis in Iowa and one that had her closing the gap with Trump in New Hampshire.

The narrow divide in Monday's caucus results between her and DeSantis means that no candidate can claim the clear mantle of Trump alternative.

Haley has turned her focus to New Hampshire, where the GOP primary is set for Jan. 23. Haley's campaign is betting big on a performance next Tuesday that could propel her campaign forward.

Both Haley and DeSantis vowed to carry on after losing to Trump in the Iowa caucuses.

"We're gonna make you proud, and we're off to New Hampshire," Haley told supporters Monday night.

On Monday night, Haley's campaign released a memo that said she would take on Trump and Biden and "go the distance in a long campaign."

"The Iowa results and the New Hampshire polls show Donald Trump is more vulnerable than commonly believed. He is the polarizing figure he has long been," campaign manager Betsy Ankeny wrote in the memo. "Trump and Biden are the two most disliked politicians in America."

ABC News' Nicholas Kerr contributed to this report.