WASHINGTON — Representative Liz Cheney of Wyoming waded deeper into Republicans’ identity crisis on Sunday, warning her party on the eve of a Senate impeachment trial not to “look past” former President Donald J. Trump’s role in stoking a violent attack on the Capitol and a culture of conspiracy roosting among their ranks.

In her first television interview since fending off an attempt by Mr. Trump’s allies to oust her from House leadership over her vote to impeach him, Ms. Cheney said Republican voters had been “lied to” by a president eager to steal an election with baseless claims of widespread voter fraud. She cautioned that the party risked being locked out of power if it did not show a majority of Americans that it could be trusted to lead truthfully.

“The notion that the election had been stolen or that the election was rigged was a lie, and people need to understand that,” Ms. Cheney said on “Fox News Sunday.” “We need to make sure that we as Republicans are the party of truth, and that we are being honest about what really did happen in 2020 so we actually have a chance to win in 2022 and win the White House back in 2024.”

She added that Mr. Trump “does not have a role as a leader of our party going forward.”

The remarks made plain that Ms. Cheney, a leading Republican voice trying to push the party back toward its traditional policy roots, had no intention of backing off her criticism of the former president after two attempts last week to punish her for her impeachment vote. In Washington, her critics forced a vote to try to oust her as the chairwoman of the House Republican conference, but it failed overwhelmingly on a secret ballot. And on Saturday, the Wyoming Republican Party censured her and called for her resignation.

Answering that call, Ms. Cheney said on Sunday that she would not resign and suggested that Republicans in her home state continued to be fed misinformation about what had taken place. It came a few days after she privately rebuffed a request by the House Republican leader, Representative Kevin McCarthy of California, to apologize to her conference for how she handled herself around the impeachment vote, according to two people familiar with the exchange, which was first reported on Sunday by Axios.

“People in the party are mistaken,” she said on Fox News of the Jan. 6 attack, which, together with nearby protests, killed five people, including a Capitol Police officer. Referring to the Black Lives Matter movement, she added: “They believe that B.L.M. and antifa were behind what happened here at the Capitol. That’s just simply not the case, it’s not true, and we’re going to have a lot of work we have to do.”

Firsthand accounts, video, criminal records and swaths of other evidence leave no doubt that supporters of Mr. Trump perpetrated the attack, believing that they could stop Congress from formalizing President Biden’s election victory.

Though she declined to say if she would vote to convict Mr. Trump were she a senator, Ms. Cheney urged Republicans to carefully consider the charge and the evidence. She also raised the possibility that a tweet that Mr. Trump had sent as the violence began to unfold criticizing former Vice President Mike Pence for refusing to try to single-handedly overturn the election result was “a premeditated effort to provoke violence.”

“What we already know does constitute the gravest violation of his oath of office by any president in the history of the country, and this is not something that we can simply look past or pretend didn’t happen or try to move on,” Ms. Cheney said. She urged her party to “focus on substance and policy and issues” rather than remain loyal to Mr. Trump.

That message is not likely to go over well with wide swaths of Republicans. Public opinion surveys suggest that Mr. Trump remains the most popular national figure in his party by far, and Republican senators appear to be lining up overwhelmingly to acquit him of the “incitement of insurrection” charge that Ms. Cheney backed.

Ms. Cheney also leveled sharp criticism at Representative Marjorie Taylor Greene, a freshman Republican from Georgia, whose past embrace of QAnon and a range of anti-Semitic and Islamophobic conspiracy theories roiled the House last week. Ms. Cheney said Ms. Greene’s views “do not have any place in our public discourse.”

“We are the party of Lincoln,” Ms. Cheney said. “We are not the party of QAnon or anti-Semitism or Holocaust deniers, or white supremacy or conspiracy theories.”

Some prominent Republican senators backed Ms. Cheney on Sunday, saying they would carefully consider the impeachment case and seek to steer the party back toward conservative policy arguments rather than personality.

“Our party is right now, if you will, being tried by fire,” said Senator Bill Cassidy, Republican of Louisiana. “We win if we have policies that speak to that families sitting around the table.”

Senator Patrick J. Toomey, Republican of Pennsylvania, said he was “really encouraged” by the House’s vote to keep Ms. Cheney in her leadership role. “They could have voted any way they felt right, and they maintained her role,” he said on “State of the Union” on CNN. “That’s how you begin to keep this party united and together and think about how we move on in the post-Trump era.”

But Ms. Cheney, the daughter of a storied Republican family in Wyoming — her father, Dick Cheney, also represented the state in the House before he was vice president — still faces the likelihood of a motivated primary challenge for the 2022 election.

And last week, even as they wagged their fingers at Ms. Greene, a vast majority of Ms. Cheney’s own House Republican conference refused to punish her. Ms. Greene emerged a day after the vote declaring she had been “freed” to push her party rightward.

“The party is his,” Ms. Greene said, referring to Mr. Trump. “It doesn’t belong to anybody else.”

Chris Cameron contributed reporting.