The Duke of York has said he has "no recollection" of meeting the woman who claims she was forced into a sexual encounter with him.
Andrew also said that he "let the side down" over his relationship with paedophile Jeffrey Epstein as he gave a "no holds barred" interview with BBC Two's Newsnight programme.
During the interview, filmed at Buckingham Palace on Thursday, the duke faced questions about his links with the disgraced financier, who was found dead in his prison cell in New York earlier this year where he was being held on sex trafficking charges.
Virginia Giuffre is one of 16 women who say they were abused by Epstein, and she has previously claimed in court that she was forced to have sex with Andrew when she was 17.
Andrew told the BBC: "I have no recollection of ever meeting this lady, none whatsoever."
He was asked by presenter Emily Maitlis for his response to claims by Mrs Giuffre, then known as Virginia Roberts, that "she met you in 2001, she says she dined with you, danced with you at Tramp Nightclub in London. She went on to have sex with you in a house in Belgravia".
Ms Maitlis added: "You don't remember meeting her?", to which Andrew replied: "No."
Mrs Giuffre's allegations were struck from US civil court records in 2015 after a judge said they were "immaterial and impertinent".
Buckingham Palace has branded the allegations "false and without any foundation" and said "any suggestion of impropriety with underage minors" by the duke was "categorically untrue".
In the BBC interview, Andrew also said that his continued relationship with Epstein after the 66-year-old's release from an 18-month prison term in 2010 for prostituting minors "let the side down" for the royal family.
He said: "I stayed with him ... and that's the bit that ... I kick myself for on a daily basis because it was not something that was becoming of a member of the royal family and we try and uphold the highest standards and practices and I let the side down, simple as that."
The full interview, Prince Andrew And The Epstein Scandal: The Newsnight Interview, will air on BBC Two at 9pm on Saturday.
Ms Maitlis said on Twitter it was a "no holds barred" and "no questions vetted" interview.
It will be the first time the duke has answered questions on his relationship with Epstein.
In 2015, he used a public appearance at Davos in Switzerland to deny the claims.