The New York-born financier is at the centre of a controversy focusing on allegations made in court by an American woman, Virginia Roberts, who claims she was forced to have sex with a number of his friends, one of them Prince Andrew.
She claims she had sex three times with the Prince when she was 17. Prince Andrew and Buckingham Palace have repeatedly denied the claims.
Last week, speaking at Davos, the Duke of York reiterated the denial and said: "My focus is my work."
Andrew was one of numerous high-profile people who once associated with the 62-year-old Epstein. Former US president Bill Clinton and actor Kevin Spacey were both associates.
But after Epstein's conviction in 2008 of one count of soliciting sex from an underage girl and his sentencing to 18 months in jail, many high-profile figures appear to have avoided him.
Prince Andrew, however, maintained his friendship with Epstein - a contributory factor to him being asked to give up his role as Britain's trade envoy in 2011.
Epstein served 13 months before being freed and forced to register as a sex offender. It has been alleged that he received special treatment from US prosecutors after lobbying from Prince Andrew, something Buckingham Palace has also denied.
Epstein's court filing late on Monday focused on efforts to keep correspondence between his lawyers and government prosecutors private.
The lawyers said Epstein could be "irreparably harmed" if such letters and emails were made public.
They cited the 1978 US Supreme Court ruling in favour of former president Richard Nixon and his efforts to bar television networks from access to his secret White House recordings. This followed his resignation after the Watergate scandal.
"Issuing the limited protective order is precisely the type of discretionary judicial management power that this court has over its records and proceedings," said the filing by Epstein's lawyers.
"The purpose of discovery is to resolve legal disputes between parties, not to provide newsworthy material."
- Independent