Former President Trump, his attorney Rudy Giuliani, the Proud Boys and Oath Keepers conspired to violate the 1871 Ku Klux Klan Act, which prohibits any actions created to prevent Congress from carrying out its duties, when they incited the January 6 riot at the Capitol, a new lawsuit from the chairman of the House Homeland Security Committee alleged.

Other lawsuit defendants are the right-wing extremist groups the Proud Boys and the Oath Keepers, whose members have been charged in the riots.

The lawsuit, filed in district court in Washington Tuesday, was brought by the NAACP on behalf of Thompson.

Rudy Giuliani is "not now representing" former President Trump "in any legal matters", senior Trump adviser Jason Miller told CNN and Reuters on Tuesday.

Soon, additional members of Congress-including Rep. Hank Johnson of Georgia and Rep. Bonnie Watson Coleman of New Jersey-are expected to join the suit as plaintiffs.

Trump adviser Jason Miller dismissed the allegations in the lawsuit, citing Trump's acquittal in the Senate impeachment trial.

"While the majority of Republicans in the Senate abdicated their responsibility to hold the President accountable, we must hold him accountable for the insurrection that he so blatantly planned", Thompson's lawsuit says.

Despite evidence to the contrary, the suit says, the men portrayed the election as stolen while Mr Trump "endorsed rather than discouraged" threats of violence from his angry supporters in the weeks leading up to the assault on the Capitol.

A lawyer for Mr Giuliani did not immediately return an email seeking comment.

In the statement, which was released through the Save America political action committee, Trump largely blamed McConnell for the party's 2020 losses in the Senate, claiming the Senate official "did nothing" as Democrats gained control of the congressional chamber.

Here's an explanation of how Trump's leaving office affects his criminal and civil exposure.

"In this respect, because of his conduct, he is just like any other private citizen".

The two are trying to push the party in opposite directions, McConnell back toward the roots of a budget-focused, pro-trade party, while Trump, who is still backed by a large portion of the Republican voter base, advocates a more populist approach.

"Fortunately, this hasn't been used very much", Sellers said.

"Former President Trump's actions that preceded the riot were a disgraceful, disgraceful dereliction of duty", said McConnell, noting Trump is "still liable for everything he did".

Critics have said that Trump and Giuliani helped incite the attack during the "Save America" rally, where both repeated false claims that the election had been stolen.

He added Mr Giuliani "remains an ally and a friend, ' and confirmed there was "no split or divorce or anything of the sort". They may also argue, as was done during the impeachment case, that Trump's speech was protected by the First Amendment.