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3 year oldMr Gates told CNN he had "several dinners" about a philanthropy project that did not emerge, and should not have given him "credibility".
Epstein hanged himself in jail in 2019 while awaiting a sex-trafficking trial.
Mr Gates also discussed his divorce with Melinda French Gates, calling it "a source of great personal sadness".
The 65 year old, who announced in March last year he was stepping down from the Microsoft board, said he and his ex-wife were "going to try and continue" working together on the Bill & Melinda Gates Foundation.
Mr Gates was also asked whether he had regrets following allegations of workplace misbehaviour - some Microsoft employees have accused him of bullying.
He did not respond specifically, saying: "Certainly everyone does [have regrets] but it's a time of reflection, and at this point, I need to go forward."
Mr Gates's representatives have previously played down his relationship with Epstein, saying there was no business partnership or personal friendship.
He echoed that in the CNN interview, saying: "I had several dinners with him, you know, hoping that what he said about getting billions of philanthropy for global health through contacts that he had might emerge.
"When it looked like that wasn't a real thing, that relationship ended."
He did not give any timeframe for the meetings, although US media have said they were between 2011 and 2014.
That was before Epstein's arrest in 2019 on federal charges of sex-trafficking of minors, but after he had served a jail sentence following conviction in 2008 for other sex offences.
Mr Gates said: "It was a huge mistake to spend time with him, to give him the credibility of being there."
US media have said Melinda French Gates was furious at his relationship with Epstein and wanted it to end.
Speaking of his ex-wife, Bill Gates said she was "a great person, and that partnership that we had coming to an end is a source of great personal sadness".
The couple announced their split in May after 27 years of marriage.
Shortly afterwards, it emerged that Microsoft was investigating a complaint that Mr Gates had "sought to initiate an intimate relationship" with a female employee in 2000. The investigation ended after Mr Gates left the board, but Microsoft said the two were not linked.
Some former employees have also accused Mr Gates of having a hot temper, with the catchphrase "that's the stupidest {expletive] idea I've ever heard".
Former board member Maria Klawe had said "a person like Bill Gates thinks the usual rules of behaviour don't apply to him".
His representatives have also played down those comments.
Mr Gates said in his CNN interview: "My work is very important to me. Within the family, we'll heal as best we can and learn from what's happened."
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