"That's the bit that… as it were, 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."
He also said he did not recall ever meeting one of Epstein's accusers, Virginia Roberts Giuffre, who has said she was forced by Epstein to have sex with Prince Andrew.
“I have no recollection of ever meeting this lady, none whatsoever,” Prince Andrew told the BBC.
"It was a convenient place to stay," he said in the clip.
"I mean I've gone through this in my mind so many times. At the end of the day, with the benefit of all the hindsight that one could have, it was definitely the wrong thing to do. But at the time I felt it was the honorable and right thing to do," he added.
"I admit fully that my judgement was probably coloured by my tendency to be too honorable but that's just the way it is."
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"It is so rare to meet people that are able to speak from their hearts with honesty+pure real truth, that remain steadfast and strong to their beliefs," she said in a tweet accompanied by four photos of the British royal. "Andrew is a true+real gentleman and is stoically steadfast to not only his duty but also his kindness + goodness"
"At no stage during the limited time I spent with him did I see, witness or suspect any behaviour of the sort that subsequently led to his arrest and conviction," Andrew said in an August statement from Buckingham Palace that was emailed to NBC News.
"I have said previously that it was a mistake and an error to see him after his release in 2010 and I can only reiterate my regret that I was mistaken to think that what I thought I knew of him was evidently not the real person, given what we now know."
The conviction he mentioned is apparently in reference to Epstein's plea agreement in 2008 with prosecutors in Florida under which he served 13 months of an 18-month sentence for two state prostitution charges.
Prince Andrew also said in the August statement that he has "tremendous sympathy" for all those affected by Epstein's "actions and behaviour."
Giuffre filed the 2015 defamation suit against Maxwell. Court documents related to the suit that were released in August revealed that Giuffre said in a 2016 deposition that Epstein and Maxwell directed her to provide sexual services for a number of powerful men.
Giuffre released a photograph in relation to her defamation lawsuit against Maxwell which shows Prince Andrew in 2001 standing in a London apartment with his hand around her bare midriff. Maxwell is also in the photo.
Prince Andrew has not been charged with any crimes or named in any of the civil suits linked to Epstein.
Giuffre's 2015 lawsuit against Maxwell was settled out of court in 2017. The documents released in August represent only a portion of the case file and offer limited context in many places.
Giuffre's allegations against Prince Andrew were struck from the court records by a judge in April 2015. However, the judge did not rule on the veracity of the claims.
In her first television interview, which aired Sept. 20 on “Dateline,” Giuffre told Savannah Guthrie she was forced to have sex with Epstein and others, including Prince Andrew.
“The first time in London, I was so young. Ghislaine woke me up in the morning and said, ‘You’re gonna meet a prince today,’” Giuffre said. “I didn’t know at that point that I was going to be trafficked to that prince. And then that night Prince Andrew came to her house in London. And we went out to club Tramp. Prince Andrew got me alcohol. It was in the VIP section. I’m pretty sure it was vodka.
"Prince Andrew was like, ‘Let’s dance together.’ And I was like, ‘OK.’ And we leave club Tramp. And I hop in the car with Ghislaine and Jeffrey. And Ghislaine said, ‘He’s coming back to the house. And I want you to do for him what you do for Epstein.’ I couldn’t believe it.”
Giuffre also said: “I couldn’t believe even royalty was involved.”
Maxwell, who has not been charged with a crime, has not commented publicly on the released court documents or on any matter related to Epstein since his arrest in July. NBC News reached out to her attorney on Friday but did not immediately hear back.
In a motion to dismiss the lawsuit prior to its being settled, Maxwell's lawyers said Giuffre "produced no evidence substantiating any of her fantastical claims that she had been trafficked by Epstein, or by Maxwell, to any of these men or any others."
A deposition by another woman, Johanna Sjoberg, which was also among the court documents released in August, also refers to Prince Andrew.
Sjoberg said in her deposition that she was a college student in 2001 when Maxwell approached her on the campus of a Florida college and offered her a job working the phones for Epstein, the court documents say. Sjoberg testified that she engaged in sex acts with Prince Andrew and Giuffre inside Epstein's mansion in Manhattan.
NBC News reached out to representatives for Prince Andrew at the time the court documents were released in August but they did not return a request for comment.
Janelle Griffith is a breaking news reporter for NBC News.