US 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 January 6, 2021 attack on the US Capitol by his supporters, told ABC's This Week that a broad movement of election denial could undermine the US 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 in Wyoming 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 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 November 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's January 6, 2021 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 January 6, 2021 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. A spokesperson for Hawley said, "We wish her the best."

Neither Cruz nor Hawley is up for re-election in November.

Cheney 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.