The New York Times on Wednesday asked a judge to unseal some legal filings that contain previously undisclosed evidence in a defamation suit brought against Fox News by Dominion Voting Systems, a company targeted with conspiracy theories about rigged machines and stolen votes in the 2020 election.

Most of the evidence in the case — including text messages and emails taken from the personal phones of Fox executives, on-air personalities, and producers in the weeks after the election — has remained under seal at the request of lawyers for the network.

Federal law and the law in Delaware, where the case is being heard, broadly protect the public’s right to access information about judicial proceedings. The law allows exceptions if a party in a lawsuit can show good cause to keep something under seal, such as a company seeking to protect a trade secret or financial information.

The judge in the case, Eric M. Davis, has cautioned that neither Fox nor Dominion was entitled to keep information secret for reasons not covered by those limited exceptions, including, he said last month, the fact that something “may be embarrassing.”

Dominion filed the lawsuit in early 2021, arguing that “Fox sold a false story of election fraud to serve its commercial purposes.” It is asking for $1.6 billion in damages from the network and its parent company, Fox Corporation.

Fox has defended itself by claiming that the commentary of its hosts and guests was protected under the First Amendment and that the allegations of fraud made by former President Donald J. Trump and his allies were inherently newsworthy, even if they were false.