CHEYENNE, Wyoming — Congresswoman Liz Cheney, President Trump’s fiercest Republican adversary in Congress, was defeated in a GOP primary Tuesday, falling to a rival backed by the former president in a rout that reinforced his grip on the party’s base.

The third-term congresswoman and her allies entered the day downbeat about her prospects, aware that Mr. Trump’s backing gave Harriet Hageman considerable lift in the state where he won by the largest margin during the 2020 campaign. Ms. Cheney was already looking ahead to a political future beyond Capitol Hill that could include a 2024 presidential run, potentially putting her on another collision course with Mr. Trump.

Ms. Cheney described her loss as the beginning of a new chapter in her political career as she addressed a small collection of supporters, including her father, Vice President Cheney, on the edge of a vast field flanked by mountains and bales of hay.

“Our work is far from over,” she said Tuesday evening, evoking Abraham Lincoln, who also lost congressional elections before ascending to the presidency and preserving the union.

The results — and the roughly 30-point margin — were a powerful reminder of the GOP’s rapid shift to the right. A party once dominated by national security-oriented, business-friendly conservatives like her father now belongs to Mr. Trump, animated by his populist appeal and, above all, his denial of defeat in the 2020 election.

Such claims, which have been roundly rejected by federal and state election officials along with Mr. Trump’s own attorney general and judges he appointed, transformed Ms. Cheney from an occasional critic of the former president to the clearest voice inside the GOP warning that he represents a threat to democratic norms. 

She is the top Republican on the House panel investigating the January 6, 2021, attack at the Capitol by Trump supporters, an attack she referenced in nodding to her political future.

“I have said since January 6 that I will do whatever it takes to ensure Donald Trump is never again anywhere near the Oval Office — and I mean it,” she said.

Four hundred miles to the east of Ms. Cheney’s concession speech, festive Hageman supporters gathered at a sprawling outdoor rodeo and Western culture festival in Cheyenne, many wearing cowboy boots, hats and blue jeans.

“Obviously we’re all very grateful to President Trump, who recognizes that Wyoming has only one congressional representative and we have to make it count,” said Ms. Hageman, a ranching industry attorney who had finished third in a previous bid for governor.

Echoing Mr. Trump’s conspiracy theories, she falsely claimed the 2020 election was “rigged” as she courted his loyalists in the runup to the election.

Mr. Trump and his team celebrated Ms. Cheney’s loss, which may represent his biggest political victory in a primary season full of them. The former president called the results “a complete rebuke” of the January 6 committee.

“Liz Cheney should be ashamed of herself, the way she acted, and her spiteful, sanctimonious words and actions towards others,” he wrote on his social media platform. “Now she can finally disappear into the depths of political oblivion where, I am sure, she will be much happier than she is right now. Thank you WYOMING!”

The news offered a welcome break from Mr. Trump’s focus on his growing legal entanglements. Just eight days earlier, federal agents executing a search warrant recovered 11 sets of classified records from the former president’s Florida estate.

Ms. Cheney’s defeat would have been unthinkable just two years ago. The daughter of a former vice president, she hails from one of the most prominent political families in Wyoming. And in Washington, she was the No. 3 House Republican, an influential voice in GOP politics and policy with a sterling conservative voting record.

Ms. Cheney will now be forced from Congress at the end of her third and final term in January. She is not expected to leave Capitol Hill quietly.

She will continue in her leadership role on the congressional panel investigating the Jan. 6 attack until it dissolves at the end of the year. And she is actively considering a 2024 White House bid — as a Republican or independent — having vowed to do everything in her power to fight Trump’s influence in her party.

With Ms. Cheney’s loss, Republicans who voted to impeach Trump are going extinct.

In all, seven Republican senators and 10 Republican House members backed Trump’s impeachment in the days after his supporters stormed the Capitol as Congress tried to certify President Biden’s victory. Just two of those 10 House members have won their primaries this year. After two Senate retirements, Senator Murkowski of Alaska is the only such Senate Republican on this year’s ballot.

Ms. Cheney was forced to seek assistance from the state’s tiny Democratic minority in her bid to pull off a victory. But Democrats across America, major donors among them, took notice. She raised at least $15 million for her election, a stunning figure for a Wyoming political contest.

Voters responded to the interest in the race. With a little more than half of the vote counted, turnout ran about 50 percent higher than in the 2018 Republican primary for governor.

If Ms. Cheney does ultimately run for president — either as a Republican or an independent — don’t expect her to win Wyoming’s three electoral votes.

“We like Trump. She tried to impeach Trump,” Cheyenne voter Chester Barkell said of Ms. Cheney on Tuesday. “I don’t trust Liz Cheney.”

And in Jackson, Republican voter Dan Winder said he felt betrayed by his congresswoman.

“Over 70 percent of the state of Wyoming voted Republican in the last presidential election and she turned right around and voted against us,” said Mr. Winder, a hotel manager. “She was our representative, not her own.”