Buckingham Palace has denied "any suggestion of impropriety with under-age minors" by Prince Andrew, after he was named in US court papers.
A woman named him in documents she filed in a Florida court over how prosecutors handled a case against financier Jeffrey Epstein.
She claims that between 1999 and 2002 she was forced by Epstein to have sex with the prince when she was a minor.
The palace said it would not comment in detail on the legal proceedings.
But a Buckingham Palace spokeswoman said: "This relates to long-standing and ongoing civil proceedings in the United States, to which the Duke of York is not a party.
"As such we would not comment on the detail. However, for the avoidance of doubt, any suggestion of impropriety with under-age minors is categorically untrue".
By Peter Hunt, BBC royal correspondent
This is a long-running, complicated legal action which began in 2011 against an American businessman called Jeffrey Epstein who has served 18 months in prison for soliciting a minor for prostitution. Back in 2011 Prince Andrew had to apologise for his friendship with Jeffrey Epstein.
In these court documents, for the first time, an unnamed woman alleges she was forced to have sexual relations with Prince Andrew when she was a minor, three times in three different locations.
He is paying a heavy price for his friendship with Jeffrey Epstein which he acknowledged at the time was a mistake on his part.
It is interesting Buckingham Palace issued this statement in the first place because in the past the Palace would not have commented on such things, they would just hope they'd go away.
Given that it was on the Politico website, it was on other national newspaper websites, I think they felt they had no choice but to make it very clear that this denial was "absolute, total and emphatic", as one of the people close to him said to me.
The woman says she was forced to have sexual relations with the prince in London, New York and on a private Caribbean island owned by Epstein.
She also claims she was forced to have sex, when a minor, with prominent lawyer and former Harvard Law professor Alan Dershowitz.
He told BBC Radio 4's Today programme: "My only feeling is if she's lied about me, which I know to an absolute certainty she has, she should not be believed about anyone else.
"We know she's lied about other public figures including a former prime minister and others who she claims to have participated in sexual activities with, so I think it must be presumed all her allegations against Prince Andrew were false as well."
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".
Her accusations are contained in a motion filed in a Florida court this week, which is part of a legal case over how federal prosecutors handled the case of Epstein.
The court document, first reported on by Politico Magazine, alleges: "Epstein also sexually trafficked the then-minor Jane Doe (a name used in US legal proceedings for people with anonymity), making her available for sex to politically connected and financially powerful people.
"Epstein's purposes in 'lending' Jane Doe (along with other young girls) to such powerful people were to ingratiate himself with them for business, personal, political, and financial gain, as well as to obtain potential blackmail information."
By Rajini Vaidyanathan, BBC Washington correspondent
While accusations are levelled against Prince Andrew, it's important to note that he is not party to the proceedings.
Instead he is named as part of evidence relating to a wider case of an alleged sex trafficking scheme, involving US businessman Jeffrey Epstein, who spent time in jail in 2008-9 for a sex offence with a minor. Two women (known as Jane Doe #1 and Jane Doe #2) are suing the US government, saying it failed to protect their rights when it entered into a plea deal with Epstein.
Now, two further women (Jane Doe #3 and #4) want to join this case, and it's Jane Doe #3 who has made claims against the Duke of York, as part of this.
The prince strongly denies the allegations. This is the first time they have surfaced publicly, and no legal case has been made against him on this matter.
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 has previously been criticised for his former friendship with Epstein, who was convicted of sex offences in 2008.
The pair were photographed meeting in December 2010, after the tycoon had served an 18-month prison sentence for soliciting a minor for prostitution, and the prince had also visited Epstein at his Florida home over the years.
The prince stepped down as the UK special representative for trade and investment in July 2011 after 10 years in the role.