He was also said to have texted: “I hate him passionately, I blew up at Peter Navarro today in frustration. I actually like Peter. But I can’t handle much more of this.”
Mr Navarro was an economic adviser to Mr Trump.
Fox News, which strongly disputed the filing, said in a statement: “Thanks to today’s filings, Dominion has been caught red-handed using more distortions and misinformation in their PR campaign to smear Fox News and trample on free speech and freedom of the press.
“We already know they will say and do anything to try to win this case, but to twist and even misattribute quotes to the highest levels of our company is truly beyond the pale.”
Dominion has accused the network of knowingly airing false claims about the election.
Fox News has called for the case to be dismissed as protected by the US First Amendment. It has also accused Dominion of cherry-picking and taking out-of-context messages sent by its senior figures.