Ms Cheney (56), the daughter of former vice-president Dick Cheney, had emerged as Mr Trump’s most prominent critic within the party and has been a driving force on the committee investigating the 2021 US Capitol riot.
She was crushed by Harriet Hageman, Mr Trump’s handpicked selection, as Republicans in Wyoming chose a candidate to run for Congress in the midterm elections in November. Ms Cheney had held the seat since 2016.
Ms Cheney immediately indicated if Mr Trump ran for the US presidency in 2024 then she could enter the race against him, either as a Republican or an independent.
She also announced the launch of a group called The Great Task, which will be dedicated to stopping Mr Trump getting back into the White House.
Mr Trump called her a “fool”, and said her defeat was “a wonderful result”.
“Liz Cheney should be ashamed of herself, the way she acted, and her spiteful, sanctimonious words and actions towards others. Now she can finally disappear into the depths of political oblivion,” he said.
Mr Trump said the result should be viewed as a referendum on, and “complete rebuke” of, the January 6 Committee, and called for it to be dissolved. He said: “The people have spoken!”
Ms Cheney was one of 10 rebel Republicans in the House of Representatives who voted to impeach Mr Trump over the Capitol riot on January 6 last year.
Of those, four have retired rather than seek re-election in November, and three have now lost to Trump-backed opponents in Republican primaries. Only two will be standing again in the mid-term elections.
Asked about a 2024 run for the White House, Ms Cheney said: “It is something that I am thinking about and I’ll make a decision in the coming months.
“I believe that Donald Trump continues to pose a very grave threat and risk to our republic. And I think that defeating him is going to require a broad and united front of Republicans, Democrats and independents. And that’s what I intend to be part of.”
She accused the former US president of “betraying Republican voters” and “lying to them” about the result of the 2020 election.
Despite raising huge sums of campaign money from supporters, Ms Cheney secured only 29pc of the vote to Ms Hageman’s 66pc.
Her defeat marked the end of the Cheney family’s four-decade political association with the “Cowboy State”, a Republican stronghold.
Donald Trump continues to pose a very grave threat and risk. Defeating him is going to require a broad and united front of Republicans, Democrats and independents
In a speech on a Wyoming cattle ranch, watched by her father, Ms Cheney said it was “the beginning of a battle” and she would “do whatever it takes to ensure Donald Trump is never again anywhere near the Oval Office”.
She added: “No American should support election deniers, for any position of genuine responsibility. Their refusal to follow the rule of law will corrupt our future.”
Ms Cheney described how Abraham Lincoln had lost races for Congress before winning “the most important election of all”. Her remark was mocked by Donald Trump Jr, who tweeted: “Liz Cheney really compared herself to Lincoln....”
Ms Hageman, a lawyer who has claimed the 2020 presidential election was “rigged” against Mr Trump, celebrated victory at a rodeo festival.
She attacked Ms Cheney for “playing a central role in the illegitimate January 6 Committee,” and said “the voters of Wyoming sent a loud message tonight”.
(© Telegraph Media Group Limited 2022)
Telegraph Media Group Limited