Nonetheless Andrew, who hosted him at Windsor Castle and remained in contact immediately following his release, is adamant it has not tarnished Britain's head of state.
Prince Andrew had a long association with Epstein, and has been accused of having sex with the billionaire's victim, Victoria Roberts Giuffre, when she was just 17.
In another cringey episode, the prince said that he does "regret the fact that [Epstein] has quite obviously conducted himself in a manner unbecoming", before the interviewer wondered if those were the proper words to describe a convicted sex offender.
The friendship allegedly led to him being introduced in 2001 to Virginia Roberts-Giuffre, who says she was trafficked by Epstein as a teenager and forced to have sex with his friends.
"I can absolutely categorically tell you it never happened", Andrew said. "Nobody can prove whether or not that photograph has been doctored".
"Prince Andrew & the Epstein Scandal" will air on BBC 2 at 9 p.m. on Saturday.
Prince Andrew also denied knowing anything about Epstein's crimes against underage girls prior to his conviction.
The Duke of York added that while Giuffre Roberts alleged that he was sweating heavily as they danceed at the nightclub, her account was erroneous as he had a medical condition at the time which meant he did not sweat.
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The senior royal's friendship with Epstein was thrown back into the spotlight this summer after court documents were released in a related defamation case.
Andrew went on to concede it was "not something that was becoming of a member of the royal family".
In this July 30, 2008 photo, Jeffrey Epstein appears in court in West Palm Beach, Florida. By then, Epstein was a registered sex offender, who'd done jail time.
She said the prince had to seek the approval of the Queen and that "she gave sign-off either late on Monday or very early on Tuesday".
The infamous photograph of Prince Andrew smiling as he stands with his left arm around the waist of a young Virginia Roberts has dogged him for years.
Last month, a private forensic pathologist hired by the Epstein family said the autopsy suggests homicide rather than suicide.
Main image: Prince Andrew at a memorial in Bruges to mark the 75th Anniversary of the liberation of the Belgian town in September.
Prince Andrew has come under increasing pressure to explain his relationship to Jeffrey Epstein, after the pair were pictured walking in Central Park together and he was spotted waving off a young woman from inside Epstein's NY home. "I have no recollection of ever meeting this lady, none whatsoever". He explained: "For the reason being that the people that I met and the opportunities that I was given to learn, either by him or because of him, were actually very useful".
He continued: "I simply - it was nearly impossible of me to sweat".
The duke denied sleeping with Mrs Giuffre on three separate occasions when quizzed by Ms Maitlis.