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LONDON — When members of the British royal family consent to warts-and-all television interviews about their troubled private lives, it generally has the effect of roiling the waters rather than calming them.

So when Prince Andrew set out to explain his friendship with the financier and convicted sex offender Jeffrey Epstein in a BBC interview broadcast Saturday night, it backfired predictably.

Viewers were left shaking their heads at the wisdom of consenting to a polite-but-relentless grilling by the journalist Emily Maitlis in the first place. Many said they found his statements alternately defensive, unpersuasive or just plain strange.

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Prince Andrew, also known as the Duke of York, repeatedly denied accusations by Virginia Roberts Giuffre that he had sex with her when she was 17 years old and had been offered to him by Mr. Epstein. Under insistent questioning by Ms. Maitlis, the duke insisted he had “no recollection” of meeting Ms. Giuffre.

But he could not explain the photograph taken in a London house that appeared to show him with his arm around the girl’s bare waist, and with Mr. Epstein’s former girlfriend, Ghislaine Maxwell, smiling in the background.

He disputed her account of an alleged meeting between him and Ms. Giuffre in a club in London. She has claimed that he sweated profusely while they danced, but he told the BBC that he could not have sweated while dancing with her at the time because he had a medical condition, dating from his combat tour in the Falklands War, that did not allow him to perspire.

He said he has since begun to sweat again.

When asked whether he regretted his relationship with Mr. Epstein, which continued after the financier served time for soliciting a minor for prostitution, Prince Andrew said: “Do I regret the fact that he has quite obviously conducted himself in a manner unbecoming? Yes.”

“Unbecoming?” the BBC interviewer, Ms. Maitlis, replied with a tone of incredulity. “He was a sex offender.”

The duke quickly backtracked, saying: “Yeah, I’m sorry, I’m being polite. I mean, in the sense that he was a sex offender.”

The reaction in the British media and on social media was uniformly withering.

“Not one single word of remorse,” said a banner headline in The Mail on Sunday.

“No Sweat … and No Regret,” said The Sunday Mirror.

“I couldn’t have slept with teenager, I was at Pizza Express,” said The Sunday Telegraph, referring to Prince Andrew’s contention that he had taken one of his daughters to a pizza restaurant on the night in 2001 that Ms. Giuffre said they danced, drank and had sex.

The Sunday Times and other news outlets reported that Jason Stein resigned two weeks ago as the prince’s public relations adviser because he believed that the duke’s decision to agree to the BBC interview “could backfire.”

Public relations experts expressed bafflement at the decision of Prince Andrew, the second son of Queen Elizabeth II and Prince Philip, to prostrate himself before television cameras when his answers to the accusations Ms. Giuffre made in a legal filing and in countless newspaper interviews were so unconvincing.

In August, as other accusers stepped forward, she said of the prince, “He knows exactly what he’s done, and I hope he comes clean about it.”

In his interview, the duke cast doubt on several accusations. For example, in explaining the photograph that appeared to show him with Ms. Giuffre, he stopped short of saying the picture had been doctored, as some of his friends have suggested. But he said that he never dresses casually when in London, that he avoids public displays of affection with strangers and that he could not have been at the place the photograph was taken.

“The photograph was taken upstairs,” Prince Andrew said, “and I don’t believe I ever went upstairs.”

Perhaps even more damaging was his explanation about why he stayed with Mr. Epstein at his Manhattan mansion in 2010, after his host was released from prison. It was “convenient,” the prince said, though he insisted that he had made the visit solely to break off their relationship.

As for a photograph of Prince Andrew, now 59, walking with Mr. Epstein in Central Park that was published in The Daily Mail in August, renewing questions about the propriety of their association, the duke said with a wan smile: “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.”

“We try and uphold the highest standards and practices,” he added, “and I let the side down, as simple as that.”

Even after all the lurid details of Mr. Epstein’s trafficking in underage girls emerged in court, Prince Andrew refused to say in the BBC interview that he regretted being friends with Mr. Epstein, who killed himself in his Manhattan jail cell in August.

The prince said that Mr. Epstein had introduced him to an array of interesting people, broadening his horizons after serving in the Royal Navy and benefiting his work as a trade envoy for Britain.

Prince Andrew is not the only prominent figure called to be embarrassed by his association with Mr. Epstein. Bill Gates, the billionaire Microsoft co-founder, recently said he regretted having met with him on a few occasions.

But the duke’s relationship with Mr. Epstein was far more extensive: He visited Mr. Epstein at his homes in Manhattan and Palm Beach, Fla., as well as his private island in the Caribbean. Prince Andrew said he had also invited Mr. Epstein and Ms. Maxwell to parties at Windsor Castle and Sandringham, another royal estate.

The Duke of York said he did not notice anything untoward on any of those visits and theorized that Mr. Epstein and his staff had behaved differently when the prince was around. He even said he did not know Mr. Epstein that well, having met him through his friendship with Ms. Maxwell, a British socialite.

Prince Andrew acknowledged that Ms. Giuffre’s accusations had taken a toll on his family, overshadowed his charity work and cast a legal shadow over him. Even as she and others have called on him to repeat his denials in court, he said he would have to consult lawyers before doing so under oath.

But if his goal in going before the cameras was to put an unpleasant episode behind him, Prince Andrew perhaps could have learned from the experiences of his older brother, Prince Charles, and his late sister-in-law, Princess Diana.

Charles, the Prince of Wales, cooperated with a wide-ranging interview with the journalist Jonathan Dimbleby in 1994 that was dominated by his confession that he had been unfaithful to his wife. A year later, Diana famously told another interviewer, Martin Bashir, that “there were three of us in this marriage,” referring to Prince Charles and Camilla Parker-Bowles, who later became his wife.

Last month, Prince Harry and his wife, Meghan, also opened up to the TV interviewer Tom Bradby. She said she was struggling with being a royal and a new mother. And Prince Harry kindled rumors of a rift in the royal family by saying that he and his brother, Prince William, were on “different paths at the moment.”

He added, “I will always be there for him as I know he will always be there for me.”