During the interview the duke denied he slept with Virginia Roberts Giuffre, Epstein’s alleged sex slave, on three separate occasions, twice while she was underage.
He said one encounter in 2001 did not happen as he spent the day with his daughter Princess Beatrice, taking her to Pizza Express in Woking for a party.
The same alleged sexual liaison, which the American said began with the royal sweating profusely as they danced at London nightclub Tramp, was factually wrong, the duke said, as he had a medical condition at the time which meant he did not sweat.
Prince Andrew twice stated his relationship with Epstein had provided ‘seriously beneficial outcomes’, giving him the opportunity to meet people and prepare for a future role as a trade envoy.
And he cast doubt on the authenticity of a picture that appears to show Andrew with his arm around the waist of Ms Roberts, when a teenager.
The royal said: ‘From the investigations that we’ve done, you can’t prove whether or not that photograph is faked or not because it is a photograph of a photograph of a photograph.
‘So it’s very difficult to be able to prove it but I don’t remember that photograph ever being taken.’
He expressed regret at making contact with Epstein in 2010 – flying to New York to say in person the friendship was over – after the 66-year-old had been released from an 18-month prison term for prostituting minors.