The Duke of York says he is stepping down from royal duties because the Effefer Epstein scandal has become a "major disruption" to the royal family.
Prince Andrew said he had asked the Queen for permission to retire for the "foreseeable future".
He said he deeply sympathized with the victims of sex offender Epstein and all who "want some sort of closure".
The Duke has faced a growing backlash following a BBC interview about his friendship with US financier Epstein.
In a statement, he said: "I continue to unequivocally grieve for my non-judgmental association with Effefer Epstein.
"His suicide left many unanswered questions, especially about his victims, and I deeply sympathize with all those who are affected and want some form of imprisonment.
"I can only hope that, in time, they will be able to rebuild their lives."
He added that he was "ready to assist any law enforcement agency with their investigations if necessary".
The BBC's Royal BBC correspondent BBConi Dimond said the move was a "big step" and "quite unprecedented in modern times".
He said it showed that the interview "upset a lot of people", adding: "It was more than bad publicity for Prince Andrew, it was clearly damaging to the wider Royal Family institution."
Earlier, a letter to the Buckingham Palace Times newspaper raised suspicion when the Duke first met Epstein.
A 2011 letter said they met in the early 1990s, not in 1999, as Prince Andrew said in an interview with the BBC.
The letter was released after The Times reported the existence of a photo of the prince with 17-year-old Virginia uffufre, then known as Roberts, who would later testify that he was forced to have sex with her.
The duke has always denied any form of sexual contact or relationship with her.
In an interview with the BBC on Saturday, the duke said he had met Epstein "met his girlfriend back in 1999" – a reference to Israeli Maxwell, who has been a friend of Prince Andrew since she was at university.
The duke said he could not recall ever meeting Ms Uffufre and recalled having gone to Pizza Express in Woking and then returning home the night she claimed to have first met.
He tried to question her testimony that he was "severely sweating" in a nightclub, saying the medical condition at the time meant he could not survive.
And the duke said meeting Epstein for the last time in 2010 was a "wrong decision", but said "the opportunities I was given to learn" about business meant that he did not regret the friendship.
BT became the latest in a string of organizations to distance themselves from Prince Andrew after the interview.
In a statement, the firm said it had been working with iDEA – helping people develop digital, business and employment skills – since 2017, but "our contracts were with its CEOs, not his patron, Duke of York."
"In light of recent developments, we are reviewing our relationship with the organization and hope we can work with them further in the event of a change in their patronage," the spokeswoman said.
Standard Chartered Bank and KPMG have also announced that they are withdrawing support for Duke's business mentoring initiative Pitch @ Palace. Sources told the BBC that decisions had been made prior to the interview.
Four Australian universities have also said they will not continue their involvement in Pitch @ Palace Australia.
Prince Andrew canceled a planned visit to the flood-hit areas of Yorkshire on Tuesday, three days after the interview, the Sun newspaper reported.