Lawyers representing more than 20 media companies on Monday asked the Florida judge overseeing the trial of George Zimmerman, the neighborhood watch organizer who killed the teenager Trayvon Martin, to unseal the court file.

The Seminole County judge who presided over Mr. Zimmerman’s brief court appearance on Thursday agreed to a request by Mark M. O’Mara, Mr. Zimmerman’s lawyer, to keep documents related to the case private. State Attorney Angela B. Corey did not object to Mr. O’Mara’s request during the hearing.

In an eight-page motion, the lawyers for the media companies, which included The New York Times Company, argued that the records were improperly sealed because Mr. O’Mara did not submit evidence showing that closing them was necessary to prevent a “serious and imminent” threat to the administration of justice.