Cheney, R-Wyo., also blasted House Republicans for elevating Rep. Elise Stefanik of New York to replace her in party leadership, calling it "dangerous" to promote yet another leader who has promoted Trump’s falsehoods about the 2020 election.
"What does it say about the party choosing somebody to replace you, who was effectively chosen by Donald Trump and saying what he's been saying - those very lies you were talking about?" Karl asked Cheney in the interview, which will air in full on "This Week" on Sunday.
"I think it's dangerous. I think that we have to recognize how quickly things can unravel," Cheney told Karl. “We have to recognize what it means for the nation to have a former president who has not conceded and who continues to suggest that our electoral system cannot function, cannot do the will of the people."
After an unsuccessful attempt in February, Republicans, with the backing of GOP leaders, removed Cheney from the No. 3 party leadership post in a closed-door vote Wednesday amid her repeated criticism of Trump and his comments about the 2020 election.
On Friday, the conference overwhelmingly appointed Stefanik, who was endorsed for the position by Trump, to fill her role. Stefanik has also promoted some of the unfounded conspiracy theories questioning the election results in Arizona and voted against the election results in Pennsylvania on the House floor on Jan. 6.
"Frankly, it's the same kinds of things that the Chinese Communist Party says about democracy: that it's a failed system, and America is a failed nation," Cheney said of Trump’s election comments promoted by many Republicans. "I won't be part of that. And I think it's very important for Republicans who won't be part of that to stand up and speak out."
Cheney’s leadership position was called into question earlier this year when she voted to impeach Trump following the deadly attack on the U.S. Capitol on Jan. 6. She was one of only 10 House Republicans who voted to do so.
Since that attack, Cheney has been an outspoken opponent of Trump’s, blaming him for inciting violence that day and painting him as a threat to democracy.
"I think the issue really is Donald Trump and it really is the party and whether we're going to be a party that's based on the truth," Cheney said. "I think we've seen consistently since the election, certainly since Jan. 6 and in ways, it's increased since Jan. 6, the former president's willingness to be very aggressive in his attacks on democracy and on our electoral process."
The events of Jan. 6 remain a central focus for lawmakers in both chambers. After months of negotiations, a bipartisan pair of House lawmakers announced an agreement to form a bipartisan commission to investigate the Capitol attack and its aftermath.
While Democrats are expected to bring the measure to the House floor next week, House Minority Leader Kevin McCarthy, R-Calif., told reporters he had not reviewed the proposal.
Cheney: McCarthy 'absolutely' should testify about Jan. 6
Cheney told Karl that McCarthy "absolutely should" testify before any commission, and that she "wouldn't be surprised if he were subpoenaed."
"I think that he very clearly and said publicly that he's got information about the president's state of mind that day," Cheney said.
McCarthy spoke to Trump on Jan. 6, and reportedly told him to call off his supporters during the riot at the Capitol, according to a statement from Rep. Jamie Herrera Beutler, R-Wash., who cited a conversation with McCarthy.
Herrera Beutler said Trump replied, "'Well, Kevin, I guess these people are more upset about the election then you are.'"
McCarthy did not deny Trump’s comments but downplayed them when pressed in a Fox News interview, saying Trump was "engaged in the idea of making sure we could stop what was going on inside the Capitol at that moment in time."
"I would hope he doesn't require a subpoena, but I wouldn't be surprised if he were subpoenaed," Cheney said of McCarthy.
Aides to McCarthy, who had called for a panel to investigate political violence beyond Jan. 6, did not respond to a message seeking a response to Cheney’s comments.
"The elements of that commission are exactly as they should be. I'm very glad they rejected leader McCarthy's suggestions that somehow we should dilute the commission, it's really important that it be focused on just on January 6 and the events leading up to it," Cheney said.
Cheney's full interview with ABC News will air on "This Week" on Sunday morning.