Rupert Murdoch said Fox News hosts Sean Hannity and Laura Ingraham maybe “went too far” in their coverage of Donald Trump’s voter fraud lie, according to an email submitted as evidence in a defamation lawsuit brought by an election operations company.

Dominion Voting Systems is suing Fox News for $1.6bn, accusing the cable TV network of amplifying debunked allegations that their voting machines were used to rig the 2020 US presidential election against Trump, in favour of Joe Biden.

Documents that became public on Tuesday offered a window into Fox’s internal deliberations. They show executives, producers and hosts discussing concerns about the network’s reputation and casting doubt on the plausibility of Trump’s claims.

More than 6,500 pages were released. The full extent of the evidence is not clear as many filings are heavily redacted.

In one exhibit, Murdoch, now 91 and chairman of Fox Corporation, emailed the Fox News president, Suzanne Scott, the day after Biden’s inauguration, asking: “Is it ‘unarguable that high-profile Fox voices fed the story that the election was stolen and that January 6th an important chance to have the result overturned’? Maybe Sean and Laura went too far. All very well for Sean to tell you he was in despair about Trump, but what did he tell his viewers?”

In an earlier exchange, Murdoch wrote that it had been suggested that primetime hosts say something like “the election is over and Joe Biden won”. Murdoch told Scott some version of this would “go a long way to stop the Trump myth that the election stolen” and reasoned that Trump would “concede eventually”.

According to the Dominion filings, Murdoch emailed a friend that the notion state legislators could change the election outcome – an idea gaining traction on the right – “sound[s] ridiculous. There’d be riots like never before.”

“Stupid and damaging,” Murdoch continues, referring to a news conference by the then Trump lawyer Rudy Giuliani. “The only one encouraging Trump and misleading him. Both increasingly mad. The real danger is what he might do as president.”

In a text, Murdoch described the claims of election fraud as “really crazy stuff”.

These exhibits and other material included in Dominion’s summary judgment motion are part of the company’s effort to prove Fox News either knew the statements it aired were false or recklessly disregarded their accuracy. That is the standard of “actual malice”, which public figures must prove in defamation cases.

Federal and state election officials and Trump’s own attorney general found no fraud that could have changed the outcome of the election. Trump’s allegations have been rejected by dozens of courts, including by judges he appointed.

The lawsuit has given a stunning insight into the gap between what Fox News presented to millions of viewers and what its top stars thought and said in private, as well as their dread of losing audience to competitors.

Two days before the January 6 insurrection, the host Tucker Carlson texted a producer to say: “We are very, very close to being able to ignore Trump most nights. I truly can’t wait. I hate him passionately.”

In an exchange more than a month earlier, Carlson said what Trump “is good at is destroy[ing] things. He could easily destroy us if we play it wrong.”

Fox News argues claims by Trump and his lawyers were inherently newsworthy and protected by the constitution. The network said in a statement the newly released documents show Dominion using “distortions and misinformation” to “smear Fox News and trample on free speech”.

Fox News has said that Dominion’s “extreme” interpretation of defamation law would chill press freedom.

Its evidence includes more context of testimony and messages that it says Dominion “cherry-picked” and “misrepresented”.

For example, Fox News cites additional testimony by the Fox Corp chief executive, Lachlan Murdoch, who said under oath he was “concerned” but “not overly concerned” by declining ratings after the election.

In a reply brief, Dominion pushes back: “The charges Fox broadcast against Dominion are false. Fox does not spend a word of its brief arguing the truth of any accused statement.”

“Finally, Fox has conceded what it knew all along,” the brief reads.

The exhibits released on Tuesday had several references to accusations against Dominion made by the Trump lawyer Sidney Powell. In one email, the Fox News host Dana Perino referenced a Powell interview with another host, Maria Bartiromo, saying “this is nuts”. Carlson said in a text message: “Sidney Powell is lying.”

In another exhibit, Hannity said he was giving Powell time to produce evidence but stopped having her appear on-air after she failed to deliver. Hannity has been quoted by Dominion during a deposition as saying he “did not believe” claims by Powell “for one second”.

In his own deposition in January, Murdoch was asked by a lawyer for Dominion, “Do you believe that the 2020 presidential election was free and fair?”

The media mogul replied: “Yes.”

He added later: “The election was not stolen.”

A Dominion spokesperson said the “emails, texts, and deposition testimony speak for themselves. We welcome all scrutiny of our evidence because it all leads to the same place – Fox knowingly spread lies causing enormous damage to an American company.”

The trial, set to begin on 17 April, is slated to last five weeks. But there is little sign of it making an impact on the tone and tenor of Fox News coverage. Carlson has this week used footage of the deadly January 6 attack to falsely portray it as a largely peaceful gathering, earning rebukes from Democrats and Republicans in Congress.

Michael Steele, former chairman of the Republican National Committee, said: “It wasn’t about the country, it was about the ratings. It wasn’t about objective, honest journalism. It was about Maga [Make America great again, Trump’s slogan] propagandism.

“It’s about further ingratiation of Fox and its cohorts, the folks on TV, being loyal to Trump to the point that they were so afraid of losing him. It is like the worst, most dependent relationship in history because the consequences go beyond Fox and Trump.”

Reuters contributed reporting