|Buckingham Palace issued 2 denials of the Prince's involvement|
The Duke of York and Mr Dershowitz were named in US court papers relating to the handling of a case against financier Jeffrey Epstein.
(The Daily Mail reports that Epstein has been accused of interfering with the FBI investigation into his activities by harassing and threatening witnesses.)
Both men deny the allegations.
Buckingham Palace says the sex claims against the duke are "without any foundation".
Mr Dershowitz filed papers at a court in Florida, where the case is being heard, to contest what he described as "absolutely outrageous claims".
The former Harvard law professor has asked for his name to be removed from documents which accuse him and Prince Andrew of having sexual relations with Virginia Roberts, known in court as Jane Doe #3, who was under the age of consent in the US at the time of the alleged incidents.
|Lawyer and Harvard law professor Alan Dershowitz|
Before his papers were filed, lawyers for the woman said they stood by their story and challenged Mr Dershowitz to provide any evidence that he believed would refute their allegations.
Mr Dershowitz told the Reuters news agency: "We file a sworn declaration categorically denying the charges and proving by records and other travel documents that I could not have been in the places that she says that she had sex with me.
Someone's going to bleed
"We file a motion to intervene in the court and then we file a defamation action against the two lawyers and the woman. And then we file disbarment proceedings against the two lawyers."
|Screen grab of court documents filed by Mr Dershowitz|
However, there was little prospect of Prince Andrew following suit and providing a sworn statement of denial, he added.
BBC legal correspondent Clive Coleman said there was no constitutional bar on the prince suing and it would not be unprecedented as other members of the Royal family had done so, but generally not for libel.
"A libel trial would be about the truth of what a member of the Royal family was saying and they can get very messy particularly when they involve allegations of sexual activity," he said.
The claims made against Mr Dershowitz and the prince were part of evidence submitted in a wider case involving Epstein.
Two women, whose names have not been revealed but are referred to as Jane Doe #1 and Jane Doe #2, are suing the US government. They claim that it failed to protect their rights when it entered a plea deal with Epstein - who spent time in jail in 2008-9 for a sex offence with a minor.
Two more - Virginia Roberts and a woman known as Jane Doe #4 - now want to join the case.
|Prince Andrew, 17 year old Virginia Roberts and Ghislain Maxwell|
Maxwell has been accused of procuring underage prostitutes for VIPs
She doesn't say how she was forced, or, at least, it is not being reported. So far, none of the reporters who have covered this story have thought to ask. She was paid a lot of money though - can that be a form of coercion? I don't think so. Certainly, in the picture above, she does not resemble what I would call a 'sex-slave'.
|Recent photo of|
The prince later had to apologise for his friendship and stepped down as the UK's special representative for trade and investment.
It is understood Prince Andrew, who is fifth in line to the throne, is now back in the UK after a skiing holiday in Switzerland.
It is likely the 54-year-old's first public appearance will be at a reception at the World Economic Forum in Switzerland later this month.
A royal aide has said the prince will "move on and push ahead" with his work, describing him as "resilient".
The prince's former wife, Sarah Duchess of York, who had gone on the skiing holiday with him, has spoken out in his defence.
"He is the greatest man there is. It was the finest moment of my life in 1986 when I married him," she told reporters. "He is a great man, the best man in the world." Curious statement since they separated after 6 years of marriage. It sounds a bit disingenuous if not outright hyperbole, or is that just how Fergie talks?
London Mayor Boris Johnson said he had sympathy for the prince, when asked a question about him on his monthly LBC radio phone-in show.
"Prince Andrew does a huge amount of unsung and unheralded work for this country," he said.
"People go on and on about air miles but I have seen that guy get out there and sell this country, trying to help British firms to get business around the world."