Republican congresswoman Liz Cheney has conceded defeat in one of the most keenly watched US primary races of 2022.

Counting is continuing, but early results suggest Ms Cheney has been defeated by the Trump-endorsed candidate Harriet Hageman by a margin of about 30 per cent.

In her concession speech on a Wyoming ranch, Ms Cheney said she could easily have taken the seat for a fourth term, but she said that would have required that she go along with Donald Trump's lies about the 2020 election, which she was not prepared to do.

Ms Cheney's decision to impeach Mr Trump, coupled with her central role in the January 6 committee investigating the attack on the US Capitol has alienated Mr Trump's base and made her a virtual outcast in her own party.

The daughter of former vice-president Dick Cheney has vowed to continue to fight Mr Trump and his legacy.

Cheney looks to future with possible presidential run

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, on the edge of a vast field flanked by mountains and bales of hay.

"Our work is far from over," she said.

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.

Hinting at a presidential bid of her own, she said: "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."

The third-term congresswoman and her allies had entered the day downbeat about her prospects, aware that Mr Trump's backing gave Ms Hageman a considerable lift in the state where he won by the largest margin during the 2020 campaign.

Cheney defeat reinforces Trump's grip on party

In conceding the race, Ms Cheney said she was not willing "go along with President Trump's lie about the 2020 election" to win a primary.

"It would have required that I enable his ongoing efforts to unravel our democratic system and attack the foundations of our republic," she told a gathering of her supporters

The ousting of Ms Cheney is the latest sign of Mr Trump's enduring sway over the Republican Party.

Mr Trump, who has hinted that he will run for president in 2024, made ending Ms Cheney's congressional career a priority among the 10 House Republicans targeted for supporting his impeachment in 2021.

Ms Cheney's defeat would have been unthinkable just two years ago.

She hails from one of the most prominent political families in Wyoming.

In Washington, she was an influential voice in Republican politics and policy, with a sterling conservative voting record.

ABC/Wires