LONDON — Prince Andrew, facing intensifying scrutiny of his ties to the disgraced financier Jeffrey Epstein, broke a long silence on Saturday to say that he never saw or suspected any behavior involving the sexual trafficking and exploitation of underage girls during their long friendship.

The prince’s statement, which was issued in his own name instead of by Buckingham Palace, was by far the most comprehensive account he has offered of their friendship. Yet Prince Andrew offered no new explanation for continuing a relationship with Mr. Epstein after the financier emerged from a Florida jail in 2010 following a sex crime conviction.

The 59-year-old second son of Queen Elizabeth II has been under growing pressure since Mr. Epstein’s arrest last month in New York on sex trafficking charges. Lawyers for Mr. Epstein’s accusers have demanded that Prince Andrew disclose whatever he knows about the financier’s behavior, even more pointedly since Mr. Epstein’s suicide this month in a New York jail.

One of the accusers, Virginia Roberts Giuffre, said in legal filings in 2015 that when she was 17, Mr. Epstein lent her to Prince Andrew for sexual exploitation on multiple occasions. She has released a photograph from 2001 showing Prince Andrew standing in a London apartment with his hand around her bare midriff.