The Duke of York released a statement after new footage emerged showing him inside the convicted paedophile’s Manhattan mansion in 2010.
The video, obtained by MailOnline, was reportedly shot on December 6 2010, around the time Andrew was photographed with disgraced billionaire Epstein in New York’s Central Park.
It shows the duke looking out from a large door of the mansion waving a woman goodbye after Epstein leaves to get in a chauffeur-driven car.
A Buckingham Palace statement said: “The Duke of York has been appalled by the recent reports of Jeffrey Epstein’s alleged crimes.
“His Royal Highness deplores the exploitation of any human being and the suggestion he would condone, participate in or encourage any such behaviour is abhorrent.”
Andrew has been dogged by accusations of a lack of judgment about his links with Epstein.
The duke quit his role as UK trade envoy after fallout from the the Central Park photos.
Buckingham Palace has issued strong denials over claims from a woman who said she was forced to have under-age sex with the duke.
Virginia Roberts alleged in court papers in Florida that she was forced to have sex with Andrew when she was 17, which is under the age of consent in the state.
She alleged she had sex with Andrew “three times, including one orgy” in London, at Epstein’s New York home, and at an “orgy” on his private island in the Caribbean.
But Buckingham Palace has branded the allegations “false and without any foundation”, stating: “Any suggestion of impropriety with under-age minors” by the duke was “categorically untrue”.
Epstein, 66, killed himself in his jail cell in New York earlier this month after being charged with sex trafficking.