Federal prosecutors on Wednesday asked the judge who oversaw Ghislaine Maxwell’s sex-trafficking trial to investigate the process by which one of the jurors was chosen, after he told news outlets he was a sexual abuse victim and had discussed his experience during deliberations.

The prosecutors’ request, in a letter filed with the court, raised the possibility of additional inquiry into how jurors who voted to convict Ms. Maxwell had been selected and the prospect of Ms. Maxwell’s lawyers moving to have a mistrial declared in the closely watched case.

Later on Wednesday, Ms. Maxwell’s lawyers indicated they planned to do just that, saying in two letters to the judge that their client would seek a new trial and that the judge “can and should order” one without holding a hearing, as the government had requested.

Ms. Maxwell’s lawyers said Ms. Maxwell planned to make her request under a federal rule that grants a judge the power to grant a new trial when the “interest of justice so requires.”

The dueling requests, and the disclosure that prompted them, threatened to cloud the conviction of Ms. Maxwell, who was found guilty last month of five counts related to what prosecutors said was her role in procuring teenage girls for the disgraced financier Jeffrey Epstein to sexually abuse.

In another potential complication, a second juror described in an interview with The New York Times having been sexually abused as a child. This juror, who requested anonymity, said that they, too, had discussed the experience during deliberations and that the revelation had appeared to help shape the jury’s discussions.

The two jurors’ disclosures could be particularly problematic if they failed to note their experiences to the court during jury selection. All the potential jurors in the case were asked in a confidential questionnaire whether they or any relatives or friends had been the victim of sexual abuse or harassment.

The juror who was interviewed by the other news outlets, including The Independent and Reuters, could not immediately be reached for comment on Wednesday.

Lawyers for Ms. Maxwell did not immediately respond to requests for comment. A spokesman for the U.S. attorney’s office for the Southern District of New York declined to comment.

In their letter, federal prosecutors asked the judge in the case, Alison J. Nathan, to schedule a hearing on the matter in about a month, adding that “any juror investigation should be conducted exclusively under the supervision of the court.”

Early Wednesday evening, Judge Nathan set a schedule for motions on Ms. Maxwell’s bid for a new trial, giving the defense until Jan. 19 to file a motion and setting Feb. 2 as the government’s deadline for responding.

“The parties’ briefing should address whether an inquiry of some kind is permitted and/or required, and if so, the nature of such an inquiry,” the judge wrote. She also granted the government’s request to offer count-appointed legal counsel to the juror whose statements prompted the flurry of post-trial activity.

One immediate question in an inquiry would most likely be how the two jurors responded to the questionnaires, sent to hundreds of prospective jurors in the weeks before the trial, in Federal District Court in Manhattan.

The form included questions on a range of topics, including whether prospective jurors or members of their families had experienced sexual abuse. The prospective jurors’ responses remain under seal.

The juror who was interviewed by the other news outlets told Reuters he “flew through” the initial questionnaire and did not recall being asked about his personal experiences with sexual abuse. He said he would have answered such questions honestly, Reuters reported.

He and the second juror both made it to the next round of jury selection, appearing in court in November. There, in a process known as voir dire, Judge Nathan, drawing on their questionnaire answers, asked them several follow-up questions. Neither was asked in that setting whether they had been sexually abused, nor did they say that they had been.

Judge Nathan’s questioning of several prospective jurors, including some who wound up on the panel, indicated that they had answered “yes” to a question about whether they or a loved one had ever been the victim of a crime.

Ms. Maxwell’s lawyers said in one of their letters to Judge Nathan on Wednesday that if she decided to hold a hearing in the matter, it should be happen in less than a month. They also suggested that all 12 jurors who took part in the deliberations and verdict be questioned.

At trial, prosecutors presented two dozen witnesses and other evidence showing that Ms. Maxwell, 60, the daughter of a British media mogul, helped Mr. Epstein recruit, groom and sexually abuse underage girls. He was found dead in a Manhattan jail in 2019 while awaiting trial on sex-trafficking charges; the medical examiner ruled that Mr. Epstein had hanged himself.

The jury acquitted Ms. Maxwell of one count of enticing a minor to travel across state lines to engage in an illegal sexual act. A sentencing date has not been set.

Former federal prosecutors and legal experts said on Wednesday that the jurors’ disclosures could undermine the verdict, especially if it is shown that they did not answer the jury questionnaires or voir dire honestly.

Arlo Devlin-Brown, a former federal prosecutor who once ran the Southern District’s public-corruption unit, said, “Generally there is nothing wrong with jurors bringing their personal experiences into deliberations,” so long as they follow the judge’s instructions.

“However,” he added, “dishonesty during the selection process goes to the very integrity of the proceedings and credible allegations of such are taken very seriously.”