Prince Andrew should give sworn testimony on “everything he knows” about his friend Jeffrey Epstein after saying he was appalled by the disgraced financier’s sex crimes, lawyers for some of Epstein’s victims have said.

Representatives of women including Virginia Giuffre, who was pictured with Andrew in a now notorious photograph and alleges she was made to have sex with him, urged the prince to help them secure justice for the women Epstein abused.

“I look forward to coordinating a formal deposition where he will be given the opportunity to tell us everything he knows,” Brad Edwards, a lawyer for Giuffre, told the Guardian on Monday. “We would like to do this as soon as possible, at his convenience, and again we are very appreciative of his willingness to help.”

Epstein, 66, died this month in an apparent suicide in a New York jail cell while awaiting trial on charges of sex trafficking. He was accused of abusing underage girls and making some of them pleasure several of his rich and powerful friends.

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In a statement released on Sunday, Buckingham Palace said Andrew was “appalled by the recent reports of Jeffrey Epstein’s alleged crimes”. It said he “deplores the exploitation of any human being and the suggestion he would condone, participate in or encourage any such behaviour is abhorrent”.

Allies of Epstein’s victims noted that Andrew stood by Epstein even after some of his offending came to light. Over the weekend the Mail on Sunday published new photographs of Andrew’s visit to Epstein’s $56m home in December 2010 – two years after the money manager pleaded guilty to soliciting prostitution from a minor.

In February 2011, the News of the World ran photographs of the pair walking in Central Park during the same trip under the headline “Prince Andy and the Paedo”, setting off a storm around their friendship that has raged ever since.

There was renewed anger on Monday after the resurfacing of details of Epstein’s visit to Balmoral Castle in 1999. Andrew hosted him and his friend Ghislaine Maxwell, a daughter of the disgraced publisher Robert Maxwell, who has been accused of assisting Epstein’s abuse and denies any wrongdoing.

Giuffre 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 she alleged that she was made to have sex with Andrew among other friends of Epstein. He has always vehemently denied the allegations. 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.

Edwards said on Monday that Andrew’s latest remarks “give the impression that he will do his part to ensure the victims of Jeffrey Epstein’s crimes are able to get answers and justice”. He added: “I would like to personally help him provide these victims his assistance.”

Epstein’s 2008 guilty plea was part of a lenient deal for him and “any potential co-conspirators” to avoid further prosecution over his extensive crimes. The deal came under intense criticism for years, peaking after Donald Trump appointed Alex Acosta, the prosecutor in Florida who oversaw the deal, to his cabinet as labor secretary. Acosta resigned last month amid growing anger over his role in the case.

Under the deal, Epstein served just 13 months in jail and for much of that time was allowed out during the day to work from his office. Records released by county authorities over the weekend showed that Epstein was allowed to purchase two pairs of small women’s underwear from the jail shop during his stay.

Investigators in New York revived inquiries into Epstein after the Miami Herald newspaper published an investigative series last year. Epstein was arrested after landing at a private airport last month and prosecutors unveiled new trafficking charges against him.

The FBI continues to investigate Epstein’s abuse even after his death, raising the possibility that former friends and associates could be prosecuted. The Guardian revealed on Saturday that Jean-Luc Brunel, a French modelling scout long accused of assisting Epstein, is also alleged to have sexually assaulted models for decades. Brunel denies taking part in Epstein’s crimes and any wrongdoing in his own right.

On Monday it also emerged that Epstein had signed a will just two days before his death. The existence of the will, first reported by the New York Post, opened a new legal front in what could be a lengthy battle over his estate. Lawyers for the victims vowed to go after Epstein’s assets even if the will had named beneficiaries, as his death means there will be no trial on the criminal charges against him.

“Give his entire estate to his victims. It is the only justice they can get,” one of those lawyers, Lisa Bloom, told the Associated Press. “And they deserve it. And on behalf of the Epstein victims I represent, I intend to fight for it.”

Agencies contributed reporting