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Donald Trump hit back at Thursday, accusing him of "political theatre" after the US president assailed him in a forceful speech marking the anniversary of the .

Although Biden did not mention Trump's name, he made clear whom he was talking about in a blistering portrait of a man he said tried to cheat his way out of defeat in the 2020 election.

Biden "used my name today to try to further divide America," Trump said in a statement.

"This political theater is all just a distraction for the fact Biden has completely and totally failed," Trump said.

In his speech, Biden ripped Trump for spreading a "web of lies" claiming the 2020 vote count was fraudulent in a bid to hold onto power, and blasted the mob of the Republican's supporters who stormed the Capitol in an attempt to prevent certification of the election result.

Trump, who earlier this week cancelled a planned press conference for the anniversary, repeated his claim that the election was "rigged."

"Just look at the numbers, they speak for themselves," the former president said.

"They are not justifiable, so the complicit media just calls it the Big Lie, when in actuality the Big Lie was the Election itself."

Trump's claims of fraudulent voting and vote counts have repeatedly been rejected by the states in question, the Justice Department, and US courts.