“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,” Prince Andrew, 59, said. “And we try and uphold the highest standards and practices and I let the side down, as simple as that.”

The full interview is set to air Saturday night on BBC Two, which released excerpts from it on Friday.

The second son of Queen Elizabeth II, Prince Andrew has faced scrutiny for his ties to Mr. Epstein, the disgraced financier who faced a raft of sex trafficking and abuse charges before taking his own life in August in a Manhattan jail cell.

The glare was so intense that, after Mr. Epstein’s death, it prompted Buckingham Palace to take the rare step of issuing a statement, in which Prince Andrew said he was “appalled” by the allegations against Mr. Epstein and rejected any suggestion that the prince would take part in the “exploitation of any human being.”

While Prince Andrew expressed remorse in the interview over accepting Mr. Epstein’s invitation to stay with him, he denied allegations in a legal filing that Mr. Epstein lent one of his accusers, Virginia Roberts Giuffre, to him for sex on several occasions when she was 17.