Hosts at Fox News did not believe the allegations of voter fraud in the 2020 presidential election that were being aired on their programmes by supporters of former president Donald Trump, according to court filings in a $1.6bn (£1.34bn) defamation lawsuit against the network.

“Sidney Powell is lying” about having evidence for election fraud, Tucker Carlson wrote in a message on 16 November 2020, according to an excerpt from an exhibit that remains under seal.

The internal communication was included in a redacted summary judgment brief filed on Thursday by attorneys for Dominion Voting Systems.

Carlson also referred to Powell in a text as an “unguided missile” and “dangerous as hell”. Fellow host Laura Ingraham told Carlson that Powell was “a complete nut. No one will work with her. Ditto with Rudy”, referring to the former New York mayor and Trump supporter Rudy Giuliani.

Sean Hannity, meanwhile, said in a deposition “that whole narrative that Sidney was pushing, I did not believe it for one second”, according to Dominion’s filing.

Dominion, which sells electronic voting hardware and software, is suing Fox News and parent company Fox Corporation. Dominion says some Fox News employees deliberately amplified false claims that Dominion had changed votes in the 2020 election, and that Fox provided a platform for guests to make false and defamatory statements.

Attorneys for the cable news station argued in a counterclaim that the lawsuit was an assault on the first amendment. They said Dominion had advanced “novel defamation theories” and was seeking a “staggering” damage figure aimed at generating headlines, chilling protected speech and enriching Dominion’s private equity owner, Staple Street Capital Partners.

“Dominion brought this lawsuit to punish FNN for reporting on one of the biggest stories of the day – allegations by the sitting president of the United States and his surrogates that the 2020 election was affected by fraud,” the counterclaim states. “The very fact of those allegations was newsworthy.”

Fox attorneys also said Carlson repeatedly questioned Powell’s claims in his broadcasts. “When we kept pressing, she got angry and told us to stop contacting her,” Carlson told viewers on 19 November 2020.

Fox attorneys say Dominion’s own public relations firm expressed scepticism in December 2020 as to whether the network’s coverage was defamatory. They also point to an email from just days before the election, in which Dominion’s director of product strategy and security complained that the company’s products were “just riddled with bugs”.

In their counterclaim, Fox attorneys wrote that when voting technology companies denied the allegations being made by Trump and his surrogates, Fox News aired those denials, while some Fox News hosts offered protected opinion commentary about Trump’s allegations.

Fox’s counterclaim is based on New York’s “anti-Slaap” law. Such laws are aimed at protecting people trying to exercise their first amendment rights from being intimidated by “strategic lawsuits against public participation”, or Slapps.

“According to Dominion, FNN had a duty not to truthfully report the president’s allegations but to suppress them or denounce them as false,” Fox attorneys wrote. “Dominion is fundamentally mistaken. Freedom of speech and freedom of the press would be illusory if the prevailing side in a public controversy could sue the press for giving a forum to the losing side.”

Fox attorneys warn that threatening the company with a $1.6bn judgment would cause other media outlets to think twice about what they report. They also say documents produced in the lawsuit show Dominion has not suffered any economic harm and do not indicate that it lost any customers as the result of Fox’s election coverage.

A trial is set to begin in mid-April.