UK
4 January 2015
Last updated at 12:36 ET
The claims against Prince Andrew are "without any foundation," Buckingham Palace said
In the palace's second statement on the claims, it said those made about the duke were "without any foundation".
The Mail on Sunday has named the woman as Virginia Roberts. The BBC has not been able to verify her identity.
Palace officials made a second statement after further details about the allegations were published in Sunday newspapers.
An initial statement had said "any suggestion of impropriety with under-age minors" by the duke was "categorically untrue".
'Categorically untrue' BBC royal correspondent Peter Hunt described the latest palace denial as "quite remarkable".
He said it was understood Prince Andrew was now back in the UK after a skiing holiday in Switzerland, and it was likely his first public appearance would be at a reception at the World Economic Forum in Switzerland, later this month.
This situation "has the potential to seriously damage Prince Andrew and the institution he represents," our correspondent added.
The woman behind the allegations says she was forced to sleep with the prince when she was under age, and on three occasions - in London, New York and on a private Caribbean island owned by Epstein - between 1999 and 2002.
A US lawyer, meanwhile, says he is planning legal action against the woman.
Alan Dershowitz, who was also named in the court documents, told the BBC he wanted her claims to be made under oath.
Mr Dershowitz, a former Harvard law professor, said: "My goal
is to bring charges against the client and require her to speak in
court. 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."
'Innocent victim' Mr Dershowitz also said he thought Prince Andrew should take "whatever legal action is available" to clear his name.
He 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."
He previously told BBC Radio 4's Today programme that the allegations against Prince Andrew must be presumed to be false, and that he had only met the prince at public occasions.
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 has been criticised for his former friendship with Jeffrey Epstein (right)
The court document alleges that Epstein sexually trafficked the
woman making her available for sex to "politically connected and
financially powerful people".
Prince Andrew and Mr Dershowitz are two of three well-known men named in the court document who it alleges had sexual relations with the woman.
The prince, who is fifth in line to the throne, has previously been criticised for his former friendship with Epstein, who was sentenced to 18 months in prison for soliciting a minor for prostitution.
The prince and Epstein were photographed meeting in December 2010, after the tycoon had served his prison sentence, and the prince has also visited Epstein at his Florida home over the years.
The prince later had to apologise for his friendship and stepped down as the UK special representative for trade and investment.
US citizen Virginia Roberts waived her anonymity in an interview with the Mail on Sunday in 2011, claiming she had been sexually exploited by Epstein as a teenager.
She also claimed to have met Prince Andrew on several occasions, but the paper said there was no suggestion of any sexual contact between Virginia Roberts and the prince.
by Emily Straton and Biodun Iginla, BBC News, London
The claims against Prince Andrew are "without any foundation," Buckingham Palace said
Buckingham
Palace has "emphatically denied" Prince Andrew had sexual contact with a
woman who claims she was forced to have sex with him under age.
The Duke of York was named in US court papers relating to the handling of a case against financier Jeffrey Epstein.In the palace's second statement on the claims, it said those made about the duke were "without any foundation".
The Mail on Sunday has named the woman as Virginia Roberts. The BBC has not been able to verify her identity.
Palace officials made a second statement after further details about the allegations were published in Sunday newspapers.
An initial statement had said "any suggestion of impropriety with under-age minors" by the duke was "categorically untrue".
'Categorically untrue' BBC royal correspondent Peter Hunt described the latest palace denial as "quite remarkable".
He said it was understood Prince Andrew was now back in the UK after a skiing holiday in Switzerland, and it was likely his first public appearance would be at a reception at the World Economic Forum in Switzerland, later this month.
This situation "has the potential to seriously damage Prince Andrew and the institution he represents," our correspondent added.
The woman behind the allegations says she was forced to sleep with the prince when she was under age, and on three occasions - in London, New York and on a private Caribbean island owned by Epstein - between 1999 and 2002.
A US lawyer, meanwhile, says he is planning legal action against the woman.
Alan Dershowitz, who was also named in the court documents, told the BBC he wanted her claims to be made under oath.
Alan Dershowitz: "My goal is to bring charges against the client and require her to speak in court"
"I welcome that lawsuit. I welcome any opportunity that would put her under oath and require her to state under oath these false allegations."
'Innocent victim' Mr Dershowitz also said he thought Prince Andrew should take "whatever legal action is available" to clear his name.
He 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."
He previously told BBC Radio 4's Today programme that the allegations against Prince Andrew must be presumed to be false, and that he had only met the prince at public occasions.
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 has been criticised for his former friendship with Jeffrey Epstein (right)
Prince Andrew and Mr Dershowitz are two of three well-known men named in the court document who it alleges had sexual relations with the woman.
The prince, who is fifth in line to the throne, has previously been criticised for his former friendship with Epstein, who was sentenced to 18 months in prison for soliciting a minor for prostitution.
The prince and Epstein were photographed meeting in December 2010, after the tycoon had served his prison sentence, and the prince has also visited Epstein at his Florida home over the years.
The prince later had to apologise for his friendship and stepped down as the UK special representative for trade and investment.
US citizen Virginia Roberts waived her anonymity in an interview with the Mail on Sunday in 2011, claiming she had been sexually exploited by Epstein as a teenager.
She also claimed to have met Prince Andrew on several occasions, but the paper said there was no suggestion of any sexual contact between Virginia Roberts and the prince.
