Another committee member, former GOP Rep. Adam Kinzinger, said: "Bring it on."
President-elect Donald Trump, in his first broadcast news interview since the election, said members of the House committee that investigated the attack on the U.S. Capitol on Jan. 6, 2021, should be jailed.
"For what they did, honestly, they should go to jail," Trump told NBC's Kristen Welker on "Meet the Press."
RELATED: Trump promises pardon for Jan 6 rioters on his first day
Trump specifically singled out Rep. Bennie Thompson, the Democrat who chaired the committee, as well as former Rep. Liz Cheney, the Republican vice chair who was ostracized from her party over breaking with Trump and ousted by a Trump-backed GOP challenger. Among other things, he's accused them of deleting evidence, which the committee has vigorously denied.
Cheney hit back in a statement on Sunday: "Here is the truth: Donald Trump attempted to overturn the 2020 presidential election and seize power."
"This was the worst breach of our Constitution by any president in our nation's history," Cheney said. "Donald Trump's suggestion that members of Congress who later investigated his illegal and unconstitutional actions should be jailed is a continuation of his assault on the rule of law and the foundations of our republic."
The Jan. 6 committee, after an 18-month investigation including more than 1,000 witnesses and several public hearings, identified Trump as the "central cause" of the Capitol attack by the pro-Trump mob. The panel, made up of seven Democrats and two Republicans, voted unanimously to recommend charges to the Justice Department.
Trump has long denied any wrongdoing in connection with Jan. 6 and tried to recast the violent events as a "day of love" during his campaign. In his interview with NBC, Trump again promised, in the first day of his new administration, to look at pardons for those who've been prosecuted for their role on Jan. 6.
While Trump said he believed the Jan. 6 committee members should go to jail, he said he would not direct his top officials to prosecute them. He's tapped Kash Patel to be his FBI director and Pam Bondi to be attorney general, pending Senate approval, two allies who've made comments about going after Trump's political opponents.
"I think that they'll have to look at that. But I'm not going to. I'm going to focus on 'Drill, baby, drill,'" Trump said.
The president-elect also claimed in the interview that the House Jan.6 committee "deleted and destroyed all the evidence" related to its probe.
Cheney, in her statement, said Trump "knows his claims about the select committee are ridiculous and false, as has been detailed extensively, including by Chairman Thompson in this July 2023 letter."
Thompson defended the archival process in the letter, noting the records such as interview transcripts and video exhibits have been preserved online and can be easily accessed by the public. Thompson also noted that they were consulting with the White House and Department of Homeland Security on some information that could be sensitive to national security or to witness safety.
"There is no conceivably appropriate factual or constitutional basis for what Donald Trump is suggesting -- a Justice Department investigation of the work of a congressional committee -- and any lawyer who attempts to pursue that course would quickly find themselves engaged in sanctionable conduct," Cheney added.
Democrat Adam Schiff, who on Monday will be sworn in as a senator, responded to Trump's comments on social media.
"When Trump violated his oath, I stood up to him," Schiff wrote on X. "When he tried to overturn the 2020 election, the January 6th Committee stood in defense of our democracy. Threats to jail us will not deter us. Nothing will stop me from doing my duty to the American people."
Former Rep. Adam Kinzinger, the second Republican on the committee, also pushed back on Trump.
"Let me be clear: we did nothing wrong. The January 6 Committee's work was driven by facts, the Constitution, and the pursuit of accountability -- principles that seem foreign to Trump," Kinzinger wrote in a blog post shared on Substack.
"If Donald wants to pursue this vindictive fantasy, I say bring it on. I'm not intimidated by a man whose actions on January 6th showed a cowardly disregard for democracy and the rule of law," Kinzinger said.
President Joe Biden is said to be considering preemptive pardons for figures who may be targeted in the Trump administration, a source previously told ABC News. On the list of possible names, the source said, were Cheney and Schiff.