In his first public appearance since the claims were made, the Duke of York said he wanted to “reiterate” the denials issued by Buckingham Palace.
Prince Andrew, 54, was speaking at a World Economic Forum reception in Davos, Switzerland.
Virginia Roberts’s lawyers have repeated the claims in new documents given to a court in Florida.
The woman, who is referred to in the case as Jane Doe #3, alleges she was forced by financier Jeffrey Epstein, a convicted s** offender, to have s** with Prince Andrew when she was 17.
Buckingham Palace has previously said the claims against Prince Andrew are “categorically untrue” and lack “any foundation”.
Prince Andrew said: “Firstly I think I must, and want, for the record, to refer to events that have taken place in the last few weeks.
“I just wish to reiterate and to reaffirm the statements that have already been made on my behalf by Buckingham Palace.
“My focus is on my work and this evening’s reception allows me to tell you about just a couple of the initiatives that I have founded and am passionate about.”
The new documents, filed in Florida, mark the first time Virginia Roberts has given a statement about the allegations in her own words.
The woman’s lawyers said they had sent Prince Andrew a letter asking him to respond under oath to the allegations.
They say the letter was sent back to them as having been refused by the recipient.
The allegations against Prince Andrew emerged in evidence submitted to a US court in a case involving Jeffrey Epstein, who spent time in jail in 2008-2009.
Prince Andrew, the fifth in line to the throne, stepped down as UK trade envoy in July 2011 following controversy over his then friendship with Jeffrey Epstein.
The Duke of York is not facing any legal proceedings over the claims made in the US case.
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