WASHINGTON (AFP) - Former president Donald Trump endorsed a challenger to one of his biggest Republican critics on Thursday (Sept 9) for a primary vote seen as a key test of his continuing grip over the party.

Trump has been seeking to unseat Liz Cheney since she voted to impeach him over his role in the Jan 6 attack on the Capitol by a mob of supporters riled up by his false claims about fraud in the election he lost to President Joe Biden last November.

"I strongly endorse Republican House of Representatives candidate Harriet Hageman from Wyoming who is running against warmonger and disloyal Republican, Liz Cheney," Trump said in a statement, adding that Cheney was the Democrats' "number one provider of sound bites".

Hageman, an attorney, launched a failed bid to be the state's governor in 2018, and was once an ally of Cheney before she became an outspoken Trump critic.

"Like many Wyomingites, I supported Liz Cheney when she ran for Congress," Hageman said in a statement.

"But then she betrayed Wyoming, she betrayed this country, and she betrayed me."

The former president has endorsed primary challengers against several of the 10 House Republicans who voted to impeach him for a second time over the deadly riot at the Capitol.

Cheney, the daughter of former vice-president Dick Cheney, was seen as a rising star in the party, with hawkish foreign policy viewpoints and a conservative domestic agenda.

But she was kicked out of the party leadership in May after calling out Trump's election lies and criticising Republican colleagues for passively supporting or actively endorsing his claims.

Cheney, one of two Republicans serving on a panel created to investigate the Capitol insurrection, took to Twitter almost immediately to post a defiant response to Trump's endorsement.

"Here's a sound bite for you: Bring it," she said.