According to court documents, Giuffre accused multi-millionaire Epstein of keeping her as a teenage "sex slave". Epstein, 66, apparently committed suicide in jail awaiting trial earlier in August on charges that he abused underage girls.
The woman had already alleged in 2011 testimony that Andrew "knows the truth" about Epstein's abuse of underage girls and said he should be made to testify.
In a December 2014 court filing, Giuffre claimed that she was forced to perform sex acts with Andrew, the third child of Queen Elizabeth II and Prince Philip, and other famous men. All have denied the allegations.
Andrew, officially the Duke of York, has rejected all accusations levelled against him in connection to the Epstein case. "I deplore the exploitation of any human being and would not condone, participate in, or encourage any such behaviour," he had said in a statement last week.
In 2015, a court decided that the allegations made by Giuffre about the prince were "immaterial and impertinent" and ordered them to be struck out of a claim against Epstein.
On Tuesday, Giuffre, who now lives in Queensland with her Australian husband, spoke to reporters outside federal court in Manhattan. She is one of nearly two dozen women who spoke about alleged sexual abuse by Epstein during a court proceeding scheduled after the financier's death in prison, US media reported.
"He knows what he's done and he can attest to that," Giuffre said about Prince Andrew, a video of the press conference showed. "He knows exactly what he's done, and I hope he comes clean about it."
Brad Edwards, a lawyer representing a number of Epstein accusers, said that "with respect to Prince Andrew or anyone else who made statements, gratuitous statements, if anyone wants to come over here and talk with us, and answer real questions that the victims have, and that we have on their behalf, we welcome that invitation".
Andrew had said last week that "it was a mistake and an error to see him (Epstein) after his release (from prison) in 2010 and I can only reiterate my regret that I was mistaken to think that what I thought I knew of him was evidently not the real person, given what we now know."
The prince also said: "His suicide has left many unanswered questions and I acknowledge and sympathize with everyone who has been affected and wants some form of closure.
( With inputs from IANS )