THE woman named the Duke of York, 54, in papers filed with a Florida court last week as part of a lengthy lawsuit against American financier, Jeffrey Epstein.
The woman – identified as "Jane Doe Number 3" – claims Epstein forced her to have sex with prominent people, including Prince Andrew.
In a second statement relating to the allegations the palace said the claims are "without any foundation".
An initial statement had said "any suggestion of impropriety with under-age minors" by Prince Andrew were "categorically untrue".
According to the BBC the woman says she was forced to sleep with the Duke of York when she was under age on three occasions - in London, New York and on a private Caribbean island owned by Epstein - between 1999 and 2002.
The prince, who is Queen Elizabeth II's second son, has been criticised in the past for his relationship with 61-year-old Epstein - a registered sex offender who in 2008 was convicted of having sex with an underage girl whom he had solicited.
In 2011 Epstein made some fairly flippant remarks to the New York Post after serving 13-months of an 18-month jail stint for having sex with an underage girl.
"I'm not a sexual predator, I'm an 'offender,'" the financier told The Post.
Adding: "It's the difference between a murderer and a person who steals a bagel."
In mid-2011, the fifth in line to the throne stepped down from his role as a UK trade ambassador following some debate over his ties with the wealthy American moneyman.
Meanwhile US lawyer Alan Dershowitz, who was also named in the court documents lodged by Jane Doe Number 3, said he plans on taking legal action to clear his name.
"My goal is to bring charges against the client and require her to speak in court," Mr Dershowitz told the BBC.
"If she believes she has been hurt by me and Prince Andrew, she should be suing us for damages.
"I welcome that lawsuit. I welcome any opportunity that would put her under oath and require her to state under oath these false allegations."
While no criminal or formal charges have been made against Prince Andrew, Mr Dershowitz insisted the royal should take "whatever legal action is available" to clear his name.
Dershowitz, a Harvard Law professor, added: "You cannot allow these false allegations simply to remain out there, and you cannot allow people who make false allegations to have the freedom to continue to make them."
The woman has issued a statement through her lawyers, saying she was "looking forward to vindicating my rights as an innocent victim and pursuing all available recourse", adding that she was "not going to be bullied back into silence".
Prince Andrew is said to have enjoyed the holiday season at Swiss ski resort Verbier with his daughter Princess Eugenie.