Donald Trump has wished Ghislaine Maxwell, the British socialite and ex-girlfriend of convicted sex offender Jeffrey Epstein, "well" as she awaits trial in a high-profile case in the US.

The president was speaking at a White House press conference where he was asked by a journalist if Maxwell will "turn in powerful people", including the Duke of York.

President Trump said: "I don't know, I haven't really been following it too much.

President Donald Trump holds a mask as he speaks during a news conference at the White House, Tuesday, July 21, 2020, in Washington. (AP Photo/Evan Vucci).

"I just wish her well frankly. I have met her numerous times over the years, especially since I lived in Palm Beach and I guess they lived in Palm Beach.

"But I wish her well, whatever it is."

He added: "I don't know the situation with Prince Andrew. I just don't know. I am not aware of it."

Maxwell was told by a New York judge last week when she appeared at a court via videolink that she will remain in custody while awaiting trial on charges of trafficking minors for Epstein.

British heiress Ghislaine Maxwell, the ex-girlfriend of paedophile financier Jeffrey Epstein. Picture: Getty

Maxwell, who pleaded not guilty, will go on trial in July 2021.

Andrew stepped down from public royal life in November last year after his disastrous Newsnight interview in which he failed to show remorse over his friendship with Epstein, who took his own life while in prison.

One of Epstein's victims, Virginia Giuffre, who claims she was trafficked by the financier, alleges that Andrew had sex with her on three separate occasions, including when she was 17, still a minor under US law.

Andrew, who categorically denies any wrongdoing, has been urged to come forward and be interviewed by US prosecutors.

These calls were renewed after his friend Maxwell appeared in court accused of facilitating Epstein's sexual exploitation of underage girls.

Andrew's legal team has stressed he has made three offers to help with investigations.

Meanwhile, a lawyer for Maxwell on Tuesday asked a judge presiding over her case to impose a gag order on lawyers and others to reduce prejudicial pre-trial publicity and protect her chances of a fair trial, The Associated Press reports.

Lawyer Jeffrey Pagliuca filed a letter in Manhattan federal court citing public comments made by acting US Attorney Audrey Strauss, the head of New York's FBI office and lawyers for Maxwell's accusers after her July 2 arrest in Bradford, New Hampshire.

He said the comments showed an order was necessary to prevent "prejudicial pre-trial publicity by the government, its agents, and lawyers for alleged witnesses."

In particular, he cited comments at a news conference by William Sweeney, head of New York's FBI office, that referenced Maxwell as "one of the villains in this investigation" and compared her to a snake that "slithered away to a gorgeous property in New Hampshire."

Prosecutors declined through a spokesperson to comment on the gag order request.

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Donald Trump wishes Ghislaine Maxwell 'well' as ex-girlfriend of convicted sex offender Jeffrey Epstein awaits trial