Her sworn testimony and other evidence were collected as part of a defamation suit filed by Virginia Guiffre, who claims Maxwell and Epstein lured her into becoming the financier's sex slave when she was 16.
The lawyer said the public release of the April and July 2016 depositions should be blocked because they form the basis of criminal perjury charges in the indictment brought against Maxwell. But she also delayed the release of the depositions through Friday to give Mr Gee time to appeal.
She remains at a federal jail in Brooklyn after bail was denied because she is a risk to flee.
The charges against Maxwell came almost a year after Epstein killed himself in a Manhattan lockup where he awaited trial on sex trafficking charges.
Epstein, the disgraced financier, killed himself in a Manhattan jail cell on August 10 past year as he awaited trial for sex trafficking.
She faces up to 35 years in prison if convicted.
If not for the promise of confidentiality for her testimony, Maxwell would have invoked her Fifth Amendment right against self-incrimination during the deposition, her lawyers said.
Giuffre accused Maxwell of participating in the abuse, allegedly forcing Giuffre to have physical relations with Prince Andrew when she was a teenager.
A critical Preska said Maxwell's attorneys offered "little more than her ipse dixit", a Latin term meaning an 'unproven assertion, ' in advocating to keep the documents from being released.
They accused Ms Giuffre of leaking the deposition, and "in conjunction with the government" setting a "perjury trap" for their client, whose six criminal counts include two for perjury.
Maxwell, 58, was arrested in New Hampshire on July 2 under a six-count federal indictment from the Southern District of NY.
If the circuit courtroom doesn't organize them to stay sealed, the paperwork shall be made public Monday, in accordance to Preska's order.
Maxwell is also accused of grooming girls in the mid-1990s for Epstein's sex abuse.
To which she answered: "I don't know what you're talking about".
Last week, the judge in an already settled civil lawsuit against Maxwell from 2015 made a decision to unseal a majority of the documents in the dispute, despite her attorney's arguing that the sealed documents could "inappropriately influence potential witnesses or alleged victims".
Giuffre's lawyer, Sigrid McCawley, argued that public interest in the case "weighs in favor of unsealing Maxwell's deposition, not against it". "In the context of this case, especially its allegations of sex trafficking of young girls, the Court finds that any minor embarrassment or annoyance resulting from disclosure of Ms. Maxwell's mostly non-testimony about behavior that has been widely reported in the press is far outweighed by the presumption of public access".