The allegation surfaced in a cache of legal papers unsealed by a USA judge in a defamation case involving a British socialite alleged to have supplied Epstein with underage girls.
Giuffre said Maxwell instructed her to take off her clothes and give oral sex to Epstein the first time she met him after bringing her to Epstein's Florida home near Mar-a-Lago with the expectation she would be trained as a masseuse.
Giuffre said she did not have knowledge that Trump or Clinton ever had intimate contact with the group of girls that Epstein kept for sex. Maxwell and her representatives have previously denied she engaged in sexual abuse or sex trafficking.
In response, a spokesperson for Buckingham Palace said: "This relates to proceedings in the United States, to which The Duke of York is not a party".
Ms Giuffre had also claimed she was forced into a sexual encounter with the Duke of York.
A partial transcript of a September 2016 deposition in a lawsuit was included in hundreds of pages of documents placed in a public file by a federal appeals court in NY.
Giuffre alleged that Maxwell defamed her by claiming she was a liar.
Giuffre has said the errors were mistakes.
Contained in the defamation case papers is an allegation by a woman called Johanna Sjoberg that Prince Andrew touched her breast while they sat on a couch in Epstein's Manhattan apartment in 2001.
"It started with one and it trickled into two and so on", Virginia Guiffre, the now married Cairns mother-of-three who then went by her maiden name of Roberts, told the Miami Herald. Buckingham Palace strongly denied the allegation in 2015, saying in a statement that "any suggestion of impropriety with underage minors" by the prince was "categorically untrue".
Even after Epstein pleaded guilty to child prostitution charges in 2008, Prince Andrew refused to break off their friendship and they were photographed together following his release from prison.
In a statement to CNN last month, the spokesperson said, "The Duke of York accepts it was unwise to have met Mr. Epstein in December 2010".
Former US president Bill Clinton flew on Epstein's jet 26 times, according to the craft's log books.
In late July Epstein was found injured in his jail cell with marks on his neck.
Having dropped out of college without getting a degree, Epstein was hired to teach maths and physics at New York's exclusive Dalton School.
Asked for comment, a spokesman for Clinton said he had never been to Little St. James, the island Epstein owns in the Caribbean.