WASHINGTON (AP) — A top No Labels leader said Thursday that Republican presidential contender Nikki Haley "would deserve serious consideration" for the group's nomination if it decides to run a third-party candidate for president.

Joe Lieberman, a former Connecticut senator and co-chair of No Labels, said Haley's record as governor of South Carolina and U.N. ambassador would be a good fit for the group's plan to find a candidate in the likely event that the 2024 election becomes a rematch between Democrat Joe Biden and Republican Donald Trump.

"I think I'm speaking for a lot of No Labels members. Gov. Haley would deserve serious consideration," Lieberman said. "But that's a decision for her to make, and it's not an easy one. So we'll have to wait and see."

Haley's team said she wasn't interested in the offer.

"Nikki has no interest in No Labels, she's happy with the Republican label," said Haley campaign spokesperson Olivia Perez-Cubas.

Haley came in third in the Iowa caucuses and is banking on a strong showing in New Hampshire's primary next week to give her a path to surpass Trump, the overwhelming front-runner for the Republican presidential nomination.

Lieberman last week said he'd like former New Jersey Gov. Chris Christie, who recently ended his own GOP presidential campaign, to consider running on the No Labels ticket, calling him "the kind of candidate No Labels is looking for."

Meanwhile, former Maryland Gov. Larry Hogan quit his role as a No Labels co-chair in a move that prompted speculation he was preparing for a possible presidential campaign in the No Labels ticket. He later sought to squelch that speculation, endorsing Haley for Republican nominee.

Lieberman's comments about Haley came in response to a question before the abrupt end of a news conference in Washington where No Labels leaders called for the Department of Justice to investigate their critics. Several groups aligned with Democrats have aggressively criticized No Labels and are discouraging candidates and political operatives from working with the group, warning a third-party candidate can't win but would help Trump return to the White House.

In a letter to the head of the Justice Department's Civil Rights Division, No Labels leaders allege the campaign against them is an illegal conspiracy designed to interfere with their constitutional right to seek access to the ballot. They distinguish attacks on them from typical political commentary, which is speech protected by the First Amendment, by comparing their work to the civil rights movement.

"The alleged conspiracy to stop No Labels is a brazen voter suppression effort," Benjamin Chavis Jr., a former head of the NAACP and a co-chair of No Labels, said during the news conference.

The letter cites an array of events, most of them common political tactics or governmental decisions. A mobile billboard with a picture of Trump alongside photos of No Labels CEO Nancy Jacobson and her husband, Mark Penn, drove through their Georgetown neighborhood. A No Labels staffer said she was warned by a friend that she was endangering her career in Democratic politics by working with the group.

The Arizona Democratic Party filed an unsuccessful lawsuit challenging No Labels ballot access in the battleground state. The Maine secretary of state sent a letter to members of the new No Labels party telling them how they could change parties. A letter from the liberal group MoveOn asked other secretaries of state to investigate the group. And various critics have held meetings to discourage lawmakers, donors, candidates, political operatives and others from working with No Labels.

"This is a desperate attempt to salvage their failing campaign and keep their fleeing supporters who have finally seen through their facade," the Lincoln Project, one of the groups targeted in the letter, said in a statement.

No Labels, which has refused to disclose its donors, has qualified for the ballot in 14 states, including the battlegrounds of Arizona, Nevada and North Carolina, and is working in more than a dozen others. It plans to offer its ballot line to a "bipartisan unity ticket" as an alternative to Trump and Biden if they remain the front-runners to win their parties' nomination, saying Americans are crying out for another option.

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Cooper reported from Phoenix. Associated Press writer Meg Kinnard contributed from Columbia, S.C.

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