Updated May 5, 2021 at 5:52 PM ET

Rep. Liz Cheney, the No. 3 House Republican, is doubling down on her condemnation of former President Donald Trump over his efforts to undermine the 2020 election and his role in inciting the Jan. 6 U.S. Capitol riot as pressure mounts among top Republicans to remove her from her leadership role.

In an op-ed published Wednesday in The Washington Post, Cheney urged her party to "stand for genuinely conservative principles, and steer away from the dangerous and anti-democratic Trump cult of personality."

"Trump is seeking to unravel critical elements of our constitutional structure that make democracy work — confidence in the result of elections and the rule of law. No other American president has ever done this," the Wyoming Republican wrote.

The op-ed came the same day Trump and Rep. Steve Scalise, the second-ranking House Republican, called for Rep. Elise Stefanik of New York, a Trump loyalist, to replace Cheney as House Republican Conference chair.

The rift within the party pits Cheney, one of the most conservative members of her party, against Stefanik, one of the most ardent Trump supporters who until recently was seen as a relative moderate. It has implications for the future of the GOP, which appears to have cast its lot with the former president ahead of next year's midterm elections — even as it sidelines Cheney and other conservatives who are Trump critics.

Cheney intensified, however, her criticism of Trump and her party's support of him.

"While embracing or ignoring Trump's statements might seem attractive to some for fundraising and political purposes, that approach will do profound long-term damage to our party and our country," she wrote. "Trump has never expressed remorse or regret for the attack of Jan. 6 and now suggests that our elections, and our legal and constitutional system, cannot be trusted to do the will of the people."

Cheney, who likely faces a vote on her future as the No. 3 House Republican, insisted she will not back down.

"History is watching. Our children are watching. We must be brave enough to defend the basic principles that underpin and protect our freedom and our democratic process," she wrote. "I am committed to doing that, no matter what the short-term political consequences might be."

Her comments came the same day that Trump endorsed Stefanik for Cheney's leadership role.

"We want leaders who believe in the Make America Great Again movement, and prioritize the values of America First," Trump said in a statement. "Elise Stefanik is a far superior choice, and she has my COMPLETE and TOTAL Endorsement for GOP Conference Chair. Elise is a tough and smart communicator!"

Stefanik tweeted her thanks to Trump, writing, "We are unified and focused on FIRING PELOSI & WINNING in 2022!"

Rep. Steve Scalise also publicly called for Stefanik to replace Cheney.

"House Republicans need to be solely focused on taking back the House in 2022 and fighting against Speaker [Nancy] Pelosi and President Biden's radical socialist agenda, and Elise Stefanik is strongly committed to doing that, which is why Whip Scalise has pledged to support her for Conference Chair," Scalise's communications director, Lauren Fine, said in a statement given to NPR.

The House of Representatives is currently in recess, which means any official vote to remove Cheney from her leadership role, or elect Stefanik, would happen next week at the earliest.

On Tuesday, House Minority Leader Kevin McCarthy told Fox & Friends he's had members share concerns with him over Cheney's ability to carry out GOP messaging and pushed back that the fallout against the Wyoming lawmaker stems from her vote to impeach Trump.

"I haven't heard members concerned about her vote on impeachment, it's more concerned about the job ability to do and what's our best step forward, that we can all work together instead of attacking one another," he said.

But as Axios reported following the interview, McCarthy put it more bluntly in a moment captured on a hot mic.

"I've had it with her. I've lost confidence," he said, according to Axios.

Tensions between McCarthy and Cheney have been simmering for months as Cheney refuses to let up on rebuking Trump for undermining the 2020 election and inciting the Capitol insurrection.

But many Republicans view her fierce criticism of the former president as at odds with her role of carrying out party messaging, especially as leaders such as McCarthy and Scalise are actively working with Trump for his campaign support in the next midterm elections.

Scalise previously told Axios that Cheney's views on Trump are out of step with most Republicans.

"This idea that you just disregard President Trump is not where we are, and frankly he has a lot to offer still and has offered a lot. He wants to help us win the House back," he said.

House Majority Leader Steny Hoyer, D-Md., said Wednesday morning that Cheney's "greatest offense apparently is she is principled and she believes in the truth."

"If you're not 1,000% for Donald Trump, somehow you're not a good Republican, you're not worthy of being in the leadership," Hoyer told The Washington Post's Karen Tumulty on Post Live.

"I think it's a real weakness in the Republican Party that they have jettisoned their principles, jettisoned adherence to the truth, and simply pandered to one individual: Donald Trump."

Stefanik, 36, was first elected to the House in 2014. At the time, she was the youngest woman ever elected to Congress. A Harvard graduate who worked in the George W. Bush White House, Stefanik has shifted her political alliances from being closely aligned to the GOP's establishment wing — she was a political ally and onetime adviser to former House Speaker Paul Ryan — to a vocal Trump supporter who earned attention and praise from the former president for her role in defending him during his first impeachment trial.

Stefanik has worked for years to recruit and support more Republican women to run for Congress, a constituency in which she now enjoys a strong level of support. She has not faced a serious challenge for her upstate New York House seat since she won in 2014 and as the area has trended toward Republicans.

Copyright 2023 NPR. To see more, visit https://www.npr.org.