U.S. Representative Liz Cheney vowed on Sunday to oppose Republican candidates who back former President Donald Trump's falsehoods about a stolen 2020 election and declared Senators Ted Cruz and Josh Hawley "unfit" for office after they voted to overturn the presidential results.

Cheney, who is Trump's leading critic and vice chair of the congressional committee investigating the Jan. 6, 2021, attack on the U.S. Capitol by his supporters, told ABC's "This Week" that a broad movement of election denial could undermine the U.S. constitutional order if left unchecked.

The daughter of former Vice President Dick Cheney has already said she will spend the next two years trying to stop Trump from returning to the White House in 2024, possibly with her own presidential bid. She declined to tell ABC whether she would run inside or outside the Republican Party, should she decide to make a presidential bid.

"I'm going to be very focused on working to ensure that we do everything we can not to elect election deniers," Cheney said in an interview recorded last week, days after she lost her Republican primary race to a Trump-backed candidate.

"We've got election deniers that have been nominated for really important positions all across the country. And I'm going to work against those people. I'm going to work to support their opponents."

Cheney did not say which Republican candidates she would oppose but acknowledged that they would include some of her fellow Republicans in the House of Representatives.

Republicans are favored to take control of the House but could face a bigger challenge capturing a Senate majority in the Nov. 8 midterm elections, which will determine the balance of power in Congress for the next two years.

As one of two Republicans on the House Jan. 6 committee, Cheney has been able to draw a direct connection between the deadly melee and Trump's repeated false claims that he won the 2020 election against President Joe Biden.

"Donald Trump is certainly the center of the threat," Cheney said. "What he's created is a movement on some level that is post-truth."

The Jan. 6 assault forced Congress to temporarily suspend its certification of Trump's loss to Biden, during which Hawley, Cruz and other Republican members of Congress voted against certification of election results.

Cheney said the actions of Hawley, Cruz and other Republican lawmakers "fundamentally threatened the constitutional order and structure" and concluded that "they both have made themselves unfit for future office."

A Cruz spokesperson responded with a statement saying the senator does not want or need Cheney's endorsement.

Hawley's office was not immediately available for comment. Neither Cruz nor Hawley is up for re-election in November.

She also criticized Florida Governor Ron DeSantis for campaigning on behalf of election deniers including Republican gubernatorial candidates Kari Lake of Arizona and Doug Mastriano of Pennsylvania.

"That is something that I think people have got to have real pause about. You know, either you fundamentally believe in and will support our constitutional structure, or you don't," Cheney said.

Like Trump himself, DeSantis has flirted with voters about the possibility of his own 2024 presidential run, while he seeks reelection in Florida this year. The DeSantis campaign was not immediately available for comment.

Cheney's re-election loss in Wyoming last week was widely seen as a victory for Trump's revenge campaign against House Republicans who voted to impeach him after the Jan. 6 riot. She told ABC she heard from Biden afterwards: "We had a very good talk, a talk about the importance of putting the country ahead of partisanship."