The Duke of York also said he was "willing to help any appropriate law enforcement agency with their investigations, if required" over the Epstein probe.
In his statement, Andrew said: "It has become clear to me over the last few days that the circumstances relating to my former association with Jeffrey Epstein has become a major disruption to my family's work and the valuable work going on in the many organisations and charities that I am proud to support.
"Therefore, I have asked Her Majesty if I may step back from public duties for the foreseeable future, and she has given her permission."
The duke added: "I continue to unequivocally regret my ill-judged association with Jeffrey Epstein. His suicide has left many unanswered questions, particularly for his victims, and I deeply sympathise with everyone who has been affected and wants some form of closure.
"I can only hope that, in time, they will be able to rebuild their lives.
"Of course, I am willing to help any appropriate law enforcement agency with their investigations, if required."