A federal judge turned down pleas by ex-president Donald Trump’s former lawyers and allies to throw out more than $3bn (€2.56bn) in defamation lawsuits over false claims that a voting machine company’s technology was used to rig the 2020 presidential election.

The ruling by US District Judge Carl Nichols in Washington allows lawsuits by Dominion Voting Systems against former Trump attorneys Sidney Powell and Rudy Giuliani and MyPillow chief executive Mike Lindell to move forward.

In a written decision, Mr Nichols said that Ms Powell and Mr Lindell made their claims “knowing that they were false or with reckless disregard for the truth”.

“A reasonable juror” could conclude that Ms Powell did not have a video of Dominion’s founder saying that “he can change a million votes, no problem at all,” as she had claimed, the judge wrote.

Mr Nichols also wrote that a sensible juror could conclude that Mr Lindell’s insistence on “the existence of a vast international conspiracy that is ignored by the government but proven by a spreadsheet on an internet blog is so inherently improbable that only a reckless man would believe it,” referencing Mr Lindell’s assertion that a spreadsheet he tweeted out as proof of Mr Trump’s victory was evidence.

Mr Giuliani requested the complaint against him be dismissed for three reasons: Dominion is a corporation, it may only recover lost profits, and that the company must plead damages for its defamation claim. Mr Nichols said Dominion’s complaint does allege lost profits with specificity.

Attorneys for Dominion said “we are pleased to see this process moving forward to hold Mike Lindell, MyPillow, Rudy Giuliani, Sidney Powell, and Defending The Republic accountable”.

Defending the Republic is a group founded by Ms Powell, which has raised money to support the legal challenges she filed against the election results. Howard Kleinhendler, one of the attorneys representing Ms Powell, told The Washington Post in a statement that he and his team are “disappointed” in the court’s decision.

“We now look forward to litigating this case on its merits and proving that Ms Powell’s statements were accurate and certainly not published with malice,” he said. “We also anticipate taking full discovery of Dominion including a thorough review of its election software and machines used in the 2020 election.”

Lawyers for Mr Lindell and Mr Giuliani did not immediately respond to a request for comment.

Mr Lindell has alleged that Dominion had the “biggest crime ever committed in election history against our country and the world” and that the company had created an algorithm to flip and weigh votes in its machines, according to court documents. He also wrongly asserted the volume of votes Mr Trump received on election night broke that algorithm.

Even after public statements by election security officials and other government agencies, independent audits and paper ballot recounts to disprove his claim, he doubled down on his claims, according to the complaint filed against him.

Dominion filed separate defamation suits against Newsmax, One America News, their executives and Patrick Byrne, the former CEO of Overstock.com.