The Republican challenging Liz Cheney for a party leadership role repeated Donald Trump’s false claims that the 2020 election remains in doubt, indicating how loyalty to the former president has become the litmus test for advancement within the caucus.

Elise Stefanik, 36, a lawmaker from New York, is jockeying to be elected the next Republican conference chair in the House of Representatives as Cheney faces calls for her removal from the post over her outspoken rejection of claims that the election was stolen.

Trump on Wednesday endorsed Stefanik for the role, which would make her the party’s most senior woman on Capitol Hill, calling her a “tough and smart communicator”. He also attacked Cheney as “a warmongering fool who has no business in Republican party leadership”, in a statement issued by his Save America political action committee.

The following day, Stefanik appeared on a podcast hosted by Steve Bannon, Trump’s former adviser, and said she was “fully” supportive of Republican efforts to audit election results in Arizona, a swing state that Joe Biden won in November. Trump and his allies have sought to cast doubt on the poll despite multiple recounts.

Trump pardoned Bannon shortly before leaving the White House after federal prosecutors in New York charged the former White House strategist with defrauding hundreds of thousands of Trump supporters.

“Transparency is a good thing,” Stefanik told Bannon. “We need to fix these election security issues.”

Cheney’s disappearing clout also underscored Trump’s persistent influence in the Republican party six months after his election loss.

A staunch neoconservative and a daughter of former Republican vice-president Dick Cheney, she has said she would not support Trump if he ran again for the White House in 2024.

The 54-year-old Wyoming Republican voted to impeach Trump for his role in the January 6 attack on the US Capitol that left five people dead. She has since spoken out repeatedly against the former president and advocated for Republicans to accept the election results.

After months of haemorrhaging support from fellow Republicans, Cheney faces being kicked out of her leadership role as the third-ranking House Republican as soon as next week.

Stefanik, whose largely rural district includes much of New York state’s north country, has openly campaigned to fill the vacancy created by Cheney’s expected defenestration.

A Harvard University graduate who worked in the George W Bush administration and later advised former House Speaker Paul Ryan, Stefanik became a vocal supporter of Trump during the ex-president’s first impeachment probe in 2019. The investigation focused on Trump’s efforts to pressure Ukraine’s president to dig up dirt on Biden and his family.

In a veiled swipe at Cheney, Stefanik told Bannon that the Republican party was “one team and that means working with the president”, a reference to Trump, not Biden.

Cheney, meanwhile, has shown no signs of backing down despite losing the support of Kevin McCarthy and Steve Scalise, the number one and two House Republicans, respectively.

In an op-ed this week in The Washington Post, Cheney warned that her party was “at a turning point”, adding: “Republicans must decide whether we are going to choose truth and fidelity to the Constitution.”

“History is watching. Our children are watching. We must be brave enough to defend the basic principles that underpin and protect our freedom and our democratic process,” Cheney wrote. “I am committed to doing that, no matter what the short-term political consequences might be.”