Breaking his silence following a string of media reports about his alleged links to the financier, who killed himself in prison two weeks ago, Andrew released a statement expressing "tremendous sympathy" for Epstein's victims.
He also reiterated that it was a "mistake" seeing Epstein, 66, after the American's release from an 18-month prison term in 2010 for prostituting minors.
In a statement, Andrew said: "It is apparent to me since the suicide of Mr Epstein that there has been an immense amount of media speculation about so much in his life.
"This is particularly the case in relation to my former association or friendship with Mr Epstein.
"Therefore I am eager to clarify the facts to avoid further speculation.
"I met Mr Epstein in 1999. During the time I knew him, I saw him infrequently and probably no more than only once or twice a year. I have stayed in a number of his residences.
"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.
"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.
"I have tremendous sympathy for all those affected by his actions and behaviour.
"His suicide has left many unanswered questions and I acknowledge and sympathise with everyone who has been affected and wants some form of closure.
"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. I deplore the exploitation of any human being and would not condone, participate in, or encourage any such behaviour."