Buckingham Palace took the unusual step of issuing a statement to rebut the accusations.

“This relates to longstanding and ongoing civil proceedings in the United States, to which The Duke of York is not a party,” a palace spokesman said in a statement, using the prince’s title. “As such we would not comment on the detail. However, for the avoidance of doubt, any suggestion of impropriety with underage minors is categorically untrue.”

Image Alan M. Dershowitz Credit... Victor J. Blue for The New York Times

The motion was filed as part of a civil case involving Mr. Epstein, who was sentenced to 18 months in prison in 2008. The lawyers for two alleged victims have argued that the rights of the women were violated during the negotiation of Mr. Epstein’s plea deal. The motion requests to add two more alleged victims to the case, including the woman, identified as “Jane Doe No. 3,” who said she had sexual relations with Prince Andrew and Mr. Dershowitz when she was underage.

On Saturday, Mr. Dershowitz said he “categorically and unequivocally” denied all of the allegations. He said he would file disbarment proceedings against the lawyers who filed the motion, Bradley J. Edwards, a lawyer in Florida, and Paul G. Cassell, a former federal judge and a law professor at the University of Utah.

“They are lying deliberately, and I will not stop until they’re disbarred,” Mr. Dershowitz said in a phone interview.

Mr. Dershowitz, who served on Mr. Epstein’s legal team and is perhaps best known for representing O. J. Simpson, said he would also file an affidavit denying the claims.