The duchess subsequently accepted she had made a "gigantic error of judgment" and offered a "heartfelt" apology.
Speaking to the Evening Standard she said: "I deeply regret Jeffrey Epstein became involved in any way with me. I abhor paedophilia and any sexual abuse of children and know that this was a gigantic error of judgment on my behalf.
"I am just so contrite I cannot say. Whenever I can I will repay the money and will have nothing ever to do with Jeffrey Epstein ever again. What he did was wrong and for which he was rightly jailed."
According to sources, Epstein – clearly in denial about the scale of his crimes – was incensed by her suggestion he was a paedophile.
The billionaire was convicted in 2008 of procuring an under-age girl for prostitution and served 13 months in jail. He was facing numerous further charges of sex-trafficking earlier this year when he killed himself in his cell in New York.
In 2011 it is understood Epstein hired an unnamed firm of lawyers to sue the duchess, unless she retracted her media statement. At the same time he took on the services of crisis management PR firm Sitrick & Co to deal with the scandal over his friendship with Andrew, who was infamously photographed with the shamed billionaire following his release from prison.
The firm, which confirms it provided "consulting advice and public relations services concerning Epstein's relationship with Prince Andrew", advised him how to handle the media storm.
As a result of the outcry, the Queen's son was forced to publicly apologise and lost his job as a roving UK trade ambassador. In 2014 Sitrick sued Epstein for £65,000 ($127,500) in unpaid fees relating to their services.
In recently re-surfaced court papers, which meticulously chart what the PR firm did on Epstein's behalf, it includes a reference on March 15, 2011 to "work on statement for Fergie". Two days later, on March 17, 2011, it adds "revise suggested statement for Fergie".
A source close to the duchess said yesterday that the "for Fergie" reference relates to a statement drafted for Epstein which he was trying to get her to release.
The source added: "Epstein tried to force the duchess to release a statement retracting her suggestion that he was a paedophile which he had drafted by his PR firm.
"Epstein was very unpleasant and very aggressive. She stuck to her guns despite the pressure being put on her and refused to comply."
Eventually Epstein halted his threat of legal action.
Since his death, which led to all criminal charges being dropped, several of his alleged victims are now suing his estate for damages.
They include Virginia Roberts, who has also accused Andrew of having sexual relations with her when she was under-age, something Buckingham Palace and the prince have strenuously denied.
Andrew has also tried to distance himself from Epstein's activities, saying in a statement last month: "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 (Epstein's) arrest and conviction."
