Andrew, who is one of Queen Elizabeth II's four children, said that he first met Epstein in 1999 and had stayed at a number of his residences, but saw him no more than once or twice a year.
"At no stage during the limited time I spent with him did I see, witness or suspect any behaviour of the sort that subsequently led to his arrest and conviction," Andrew, 59, said in a statement from Buckingham Palace emailed to NBC News.
In 2008, Epstein reached a non-prosecution deal with then-Miami U.S. Attorney Alexander Acosta's office to halt a federal sex abuse investigation involving more than 30 teenage girls.
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Andrew acknowledged meeting with Epstein in 2010 after he had been released from a 13-month jail sentence for the 2008 case.
"I have said previously that it was a mistake and an error to see him after his release in 2010 and I can only reiterate my regret that I was mistaken to think that what I thought I knew of him was evidently not the real person, given what we now know," he said.
Andrew added that he had "tremendous sympathy" for Epstein's alleged victims.
"This is a difficult time for everyone involved and I am at a loss to be able to understand or explain Mr Epstein's lifestyle," he said. "I deplore the exploitation of any human being and would not condone, participate in, or encourage any such behaviour."
The royal, who also goes by his title the Duke of York, has previously faced accusations related to Epstein's alleged sex trafficking ring.
Earlier this month, he had to fend off new allegations that arose when he was mentioned in court documents unsealed in relation to a 2015 defamation lawsuit against British socialite and longtime Epstein confidante Ghislaine Maxwell by one of Epstein’s alleged victims, Virginia Roberts Giuffre.
The documents, released a day before Epstein's death, contained a deposition by Johanna Sjoberg — another woman who alleged she was forced by Maxwell to have sex with Epstein — who said that Andrew touched her breast while they sat on a couch in Epstein's Manhattan apartment in 2001.
When asked about Sjoberg’s allegations about Prince Andrew, Buckingham Palace told NBC News at the time that "any suggestion of impropriety with underage minors is categorically untrue." Buckingham Palace has also previously emphatically denied all allegations stemming from the 2015 court case.
None of the men identified by Giuffre has been charged with a crime. The suit was settled out of court in 2017.
On July 6, Epstein was arrested on sex trafficking and conspiracy charges.
Prosecutors said he sexually abused dozens of underage girls at his homes in New York and Florida in the early 2000s. Epstein was also accused of paying his victims to recruit others, allowing him to build a vast network of girls to exploit.
He pleaded not guilty and was being held without bail before his death.
Linda Givetash is a London-based freelance journalist.