“I’ve known Jeff for 15 years. Terrific guy,” Mr. Trump told New York magazine in 2002. “He’s a lot of fun to be with. It is even said that he likes beautiful women as much as I do, and many of them are on the younger side.”

He also dismissed Mr. Houraney’s warning about his friend’s conduct.

“I said, ‘Look, Donald, I know Jeff really well, I can’t have him going after younger girls,’” Mr. Houraney remembers. “He said, ‘Look I’m putting my name on this. I wouldn’t put my name on it and have a scandal.’”

Mr. Houraney said he “pretty much had to ban Jeff from my events — Trump didn’t care about that.”

Shortly before the 2016 presidential election, Mr. Houraney accused Mr. Trump himself of inappropriate behavior toward his girlfriend and business partner, Jill Harth, during their business dealings.

The White House did not respond to a request for comment on Tuesday.

But speaking Tuesday to reporters in the Oval Office, the president distanced himself from Mr. Epstein, noting that he “knew him like everybody in Palm Beach knew him.” But Mr. Trump added: “I had a falling out with him. I haven’t spoken to him in 15 years. I was not a fan of his, that I can tell you.”

Mr. Epstein, who was charged on Monday in Manhattan with sex trafficking, is better known as a longtime friend of former President Bill Clinton’s than as a close associate of Mr. Trump’s. In fact, the relationship with Mr. Trump turned so toxic that Mr. Epstein at one point told friends that he blamed Mr. Trump for his legal problems with the Palm Beach County police.

But while Mr. Trump has dismissed the relationship, Mr. Epstein, since the election, has played it up, claiming to people that he was the one who introduced Mr. Trump to his third wife, Melania Trump, though neither of the Trumps has ever mentioned Mr. Epstein playing a role in their meeting. Mrs. Trump has said that her future husband simply asked for her phone number at a party at the Kit Kat Club during Fashion Week in 1998.