Ms Giuffre claims to have been the victim of the late financier and convicted pedophile Jeffrey Epstein.
She has previously said she was forced to have sex at the age of 17 with Prince Andrew, who categorically denies any contact or sexual relationship with her.
Ms Giuffre, also known as Roberts, said in a 2016 deposition that she was forced to have sex with many rich and powerful men, including politicians, entrepreneurs, a scientist , a fashion designer and “another prince whom I don’t know his name”.
When asked if she could remember “anything else” about men, she replied, “It’s very difficult for me and very frustrating to have to go over it all. I don’t remember all the people. people I was sent to. ”
There was no indication, however, that the mysterious prince was a member of the British monarchy.
The accused men have denied the allegations.
In a manuscript written by Ms Giuffre, titled The Billionaire Playboy’s Club, she also gave more details about an alleged meeting with Prince Andrew in London.
She wrote that the Duke of York whispered “sweet things” in her ear and kissed his neck while he was on the dance floor at Tramp nightclub at a party with Epstein and his ex-girlfriend Ghislaine Maxwell.
Ms Giuffre wrote: “I would just laugh not really knowing how to respond to an aging man with a bad smile and terrible movements. ”
She said the couple bathed together at Maxwell’s, who had known Andrew from college.
Ms Giuffre wrote: “He adorned my young body, especially my feet, stroked my toes and licked my arches. ”
She alleges that they had sex, something that left her with “feelings of dismay.”
She claims to have had sex with Andrew on three occasions.
The documents come from a now-defamed defamation lawsuit filed by Ms. Giuffre and released by U.S. District Judge Loretta Preska.
Giuffre claimed in the lawsuit that Maxwell recruited her in 2000 to be Epstein’s sex maid.
Two depositions given by Maxwell remain sealed after an appeal from lawyers for the British socialite who insist the documents could make a fair trial impossible. A call on this will be heard on September 22.
Maxwell, who dated Epstein in the 1990s, is in police custody awaiting trial for child trafficking for his former partner.
She has pleaded not guilty and will be tried in July next year.
Among the documents released were emails exchanged between Maxwell and Epstein in January 2015, when Ms Giuffre’s allegations gained media attention.
Responding to an email from Maxwell, Epstein – who was then a convicted sex offender – wrote: “You haven’t done anything wrong and I urge you (you) to start acting like this. ”
He suggested that he come out and hold his head up, “not as a convict (on the run).”