Maxwell filed an emergency request with the 2nd US Circuit Court of Appeals in Manhattan one day after a federal judge rejected her claim that her need for confidentiality outweighed the public's right to see the April 2016 deposition, which was taken in a civil defamation lawsuit.
"Absent a stay from this court, it will forever let the cat out of the bag," Maxwell's lawyers wrote, noting another judge's recent refusal to block publication of former National Security Adviser John Bolton's memoir because copies had already been circulated.
Late Thursday, US District Judge Loretta Preska, who oversees the civil case, ordered the separate release of dozens of other documents that the British socialite had wanted sealed, rejecting her lawyers' bid for an emergency phone conference.
The 2016 deposition is scheduled for release on Aug. 3, unless the appeals court orders a delay or further arguments.
Maxwell, 58, has pleaded not guilty to helping Epstein recruit and eventually abuse three girls from 1994 to 1997, and committing perjury by denying her involvement under oath.
The deposition came from a now-settled lawsuit against Maxwell by Virginia Giuffre, who had accused Epstein of having kept her as a "sex slave" with Maxwell's assistance. She wants the disclosure of more information from her case.
Maxwell's lawyers have accused Giuffre of leaking the deposition, and "in conjunction with the government" setting a "perjury trap" for their client.
They said Maxwell had been promised confidentiality before being forced to answer many "personal, sensitive, and allegedly incriminatory questions," only to be sandbagged when prosecutors quoted from the deposition in her indictment.
The lawyers said this included when Maxwell responded "I don't know what you're talking about" when asked if Epstein had a scheme to recruit underage girls for sexual massages.
Maxwell was arrested on July 2 at a New Hampshire home where prosecutors said she was hiding out.
She was denied bail and is being held in a Brooklyn jail after the judge overseeing her criminal case called her a flight risk.
"The government has indicted Ghislaine Maxwell. The media has all but convicted her," Maxwell's lawyers said. "All Ms. Maxwell is asking is that this court have a fair opportunity to review the merits of the district court's decision before the deposition material is unsealed for all time."Epstein was found hanged at age 66 last August in a Manhattan jail, while awaiting trial on sex trafficking charges for abusing women and girls in Manhattan and Florida from 2002 to 2005. He had pleaded not guilty.