In her sworn affidavit, she said Buckingham Palace's forceful denial of her accusations was both false and hurtful.
Ms Roberts' lawyers also included in the legal bundle submitted to the court yesterday a letter addressed to Prince Andrew, inviting the 54-year-old to respond to the allegations in person and under oath.
The letter, dated January 14, includes a photo of the Prince with his arm around Ms Roberts which she says was taken by Mr Epstein in 2001.
The letter also refers to alleged "subsequent interactions" between Prince Andrew and Ms Roberts in New York later that year. In her affidavit, Ms Roberts reasserted her claim that she was forced to have sexual relations with the Prince on three occasions, one of which was at an orgy.
The letter to Prince Andrew was a "formal request", it said, "to interview you, under oath, regarding interactions that you had with Jane Doe No 3 beginning in approximately early 2001 ... The interview could be conducted at a time and place of your choosing, and with your co-operation, I believe the interview could be completed in two hours or less."
The letter sent by Ms Roberts' lawyers to Prince Andrew
Ms Roberts' lawyers say the letter was returned to them, apparently having been refused by its recipient.
Buckingham Palace strenuously denied the renewed allegations. When Ms Roberts' claims first emerged, the palace described them as "categorically untrue", "false" and "without any foundation" and denied the Prince and his accuser had "any form of sexual contact or relationship".
In 2011, Andrew stepped down as UK trade envoy amid controversy over his close relationship with Epstein.
This morning (NZT), the Prince is expected to appear before the cameras and address the accusations during his annual reception at the World Economic Forum in Davos.
- Independent, Telegraph Group Ltd