A letter addressed to Andrew at Buckingham Palace asking him to take part in a two-hour interview was filed yesterday in a Florida court by lawyers acting on behalf of Virginia Roberts.
Ms Roberts - who is referred to in court as Jane Doe No 3 - claims she was forced to have sex with the Duke of York when she was 17 by his financier friend Jeffrey Epstein, a convicted sex offender.
The Duke vehemently denies the claims.
The letter, dated January 14, was presented in court a day before Andrew was due to carry out his first public engagement since he was embroiled in under-age sex allegations, at the World Economic Forum in Davos.
It said: “This letter is a formal request ... to interview you, under oath, regarding interactions that you had with Jane Doe No 3 beginning in approximately early 2001. Jane Doe No 3 was then 17 years old.”
It goes on to say: “The interview could be conducted at a time and place of your choosing, and with your co-operation, I believe the interview could be completed in two hours or less.”
Prince Andrew is also asked “the favour of a prompt reply by no later than January 19”.
It was part of a legal submission containing new details about Ms Roberts’ alleged encounters with Andrew, which have been strenuously denied by Buckingham Palace.
In a sworn affadavit, Ms Roberts, who is now 31, said: “I have seen Buckingham Palace’s recent “emphatic” denial that Prince Andrew had sexual contact with me.
“That denial is false and hurtful to me. I did have sexual contact with him as I have described here - under oath.
“Given what he knows and has seen, I was hoping that he would simply voluntarily tell the truth about everything.
“I hope my attorneys can interview Prince Andrew under oath about the contacts and that he will tell the truth.”
Federal prosecutors in the US said on Tuesday that Ms Roberts and another woman claiming to be a victim of Epstein, known as Jane Doe No 4, should not be allowed to join a lawsuit seeking to reopen a plea agreement he reached in 2008.
Epstein pleaded guilty to state under-age sex and prostitution solicitation charges but escaped federal prosecution.
But prosecutors say that Ms Roberts and the other woman who sought late last year to take part in the case already brought by two other women should be barred by time limitations.
After Ms Roberts’ papers were filed in Florida yesterday, a spokeswoman said Buckingham Palace had nothing to add to its previous comments.
The Palace has stated the claims are “false and without foundation”.
It has been suggested the Duke will address the allegations during a reception today at the Swiss ski resort of Davos, home to the World Economic Forum annual gathering of economic and political movers and shakers.
It would be the first time the Duke has spoken publicly since it was claimed that he had sex with Ms Roberts on three separate occasions when she was a teenager.
A Buckingham Palace spokesman said: “We would not comment on speculation about what the Duke might say.”
Some 200 guests have been invited to the [email protected] event today, which will feature short presentations by three start-ups companies, and promote British entrepreneurship.
During his visit to the mountain village of Davos, Andrew will also attend panel debates and bilateral meetings as he has done in previous years.
Andrew stepped down as the UK’s trade envoy in July 2011 following controversy over his friendship with hedge fund tycoon Epstein.
In the legal papers, Ms Roberts says she has instructed her lawyers to “pursue all reasonable and legitimate means” to have criminal charges brought against “powerful people” whom she claims Epstein made her have sex with.
Signed “under penalty of perjury”, the affidavit adds: “Since I filed my motion in this case, my credibility has been attacked.
“I am telling the truth and will not let these attacks prevent me from exposing the truth of how I was trafficked for sex to many powerful people.
“These powerful people seem to think that they don’t have to follow the same rules as everyone else. That is wrong.”
Ms Roberts claims to have been trained to be “everything a man wanted me to be” by Epstein after she was allegedly recruited at 15 by Ghislaine Maxwell, the daughter of disgraced newspaper tycoon Robert Maxwell.
She says she had sex with Andrew “three times, including one orgy”, with the first encounter allegedly taking place in Ms Maxwell’s London townhouse.
“I knew he was a member of the British Royal Family, but I just called him Andy’,” she said of the now 54-year-old prince.
Ms Roberts allegedly had sex with Andrew a second time at Epstein’s New York mansion in spring 2001.
In her affidavit, she said: “Epstein and Maxwell were making lewd jokes about ‘Randy Andy’.
“I had the impression that Andy had come there to see Epstein and to have sex me with. There was no other apparent purpose for Andy to be there.
“I was told to go upstairs with Andy and to go to the room I thought of as the ‘dungeon’ (the massage room, but it is really scary looking).
“I had sex with Andy there. I was only paid 400 US dollars from Epstein for servicing Andy that time.”
There is no suggestion Andrew was aware Ms Roberts was being paid.
The third and final time she claims to have had sex with the Duke of York was during an alleged orgy on Epstein’s private island in the US Virgin Islands, when she was “around 18”.
“Epstein, Andy, approximately eight other young girls, and I had sex together,” she claimed.
“The other girls all seemed and appeared to be under the age of 18 and didn’t really speak English.”
Ms Maxwell has denied all the claims made against her.
A spokesman for the 53-year-old socialite said earlier this month: “The allegations made against Ghislaine Maxwell are untrue.
“The original allegations are not new and have been fully responded to and shown to be untrue.
“[The] claims are obvious lies and should be treated as such.”