WASHINGTON (AFP) - Social media has been his weapon of choice for battling Republican dissidents, but Donald Trump is seeking to tighten his iron grip on the party even after a ruling on Wednesday (May 5) extending his ban on Facebook.

Despite losing the presidency to Joe Biden last year and enduring a second impeachment in January after the deadly insurrection at the US Capitol, the brash billionaire remains his party's most influential figure - and he made clear that he knows it, demanding a leadership shake-up and reiterating his false claims of election fraud.

Trump blasted party leaders who have publicly reprimanded him, including top Senate Republican Mitch McConnell, or who voted to impeach him in January, most notably congresswoman Liz Cheney, the number three House Republican who appears increasingly likely to face removal from her leadership post.

"Liz Cheney is a warmongering fool who has no business in Republican Party leadership," Trump said in a fervid statement, adding that he wants leaders who believe in his "Make America Great Again" movement and prioritise "America First" values.

Pro-Trump New York Republican congresswoman "Elise Stefanik is a far superior choice, and she has my COMPLETE and TOTAL endorsement for GOP conference chair," he said.

Stefanik, 36, voted against certifying the election results for Biden in multiple swing states.

Trump's endorsement comes amid rising party tensions over Cheney, the most senior Republican woman in Congress, who has refused to tamp down her public denunciations of Trump.

And it all but assures that a conference-wide vote on whether to keep Cheney in the post will occur soon after lawmakers return to Washington next week.

Minutes after Facebook's independent oversight board upheld a ban on Trump - although it ordered the social media giant to further review the case - he blasted the restriction as a "total disgrace" and warned against limiting a president's freedom of speech rights.

He also issued a withering statement repeating his audacious lie that Biden and other Democrats stole the election.

Cheney "continues to unknowingly and foolishly say that there was no election fraud in the 2020 presidential election when in fact, the evidence... shows the exact opposite," Trump seethed.

"Had gutless and clueless MINORITY Leader Mitch McConnell... fought to expose all of the corruption that was presented at the time, with more found since, we would have had a far different presidential result, and our country would not be turning into a socialist nightmare."

The former president added a rallying cry to his supporters: "Never give up!"

Missing megaphone

With Trump considering another White House run, he launched a new page on his website where he pledges to present information to voters "straight from the desk of Donald J Trump".

But he no doubt misses the social media megaphone that allowed him to dominate news cycles and impulsively blast his message to more than 100 million followers.

"To be clear, if you are Trump and you want to have influence in 2022 and 2024 - and possibly run for office in 2024 - it is better to be on social media than not," Joshua Tucker, professor of politics at New York University, told AFP.

Emerson Brooking, a senior fellow at the Atlantic Council's Digital Forensic Research Lab, which focuses on exposing disinformation, said Trump's social media presence had served as a bridge linking extremists with more mainstream conservative politicians.

The ban "did remove a piece of critical connective tissue between the far-right fringe and Republican orthodoxy," Brooking said.

Trump's attacks on Wednesday appeared aimed at clipping the wings of high-profile Republicans who have not fallen in line with his false voter fraud narrative.

Cheney, a third-term congresswoman from Wyoming, is one of few congressional Republicans who openly declare Trump lost fair and square in November.

She confidently repeated the assertion on Monday, tweeting that anyone who claims the 2020 election was stolen "is spreading THE BIG LIE (and) poisoning our democratic system."

While Cheney easily won a secret ballot vote by Republicans in February, the Trump-backed challenge to her leadership role may well end with her ouster.

Top House Republican Kevin McCarthy backed Cheney in February but was recently caught on a hot mic saying he has "lost confidence" in her.

Meanwhile, House Speaker Nancy Pelosi's office, eager to paint Republicans as in thrall of Trump because of efforts to oust Cheney for speaking election truth, said McCarthy was "willing to throw our democracy under the bus if it means appeasing Trump and the far right elements of his base."