The Duke of York has "sought to falsely portray himself" as eager to cooperate with an inquiry into sex offender Jeffrey Epstein, the US prosecutor in charge of the investigation has said.
US attorney Geoffrey Berman said Prince Andrew "has repeatedly declined our request" to schedule an interview.
The duke's lawyers previously rejected claims he had not co-operated, saying he offered to help three times.
He will not be extradited, the US government's chief lawyer has said.
US Attorney General William Barr told Fox News: "I don't think it's a question of handing him over. I think it's just a question of having him provide some evidence."
Prince Andrew stepped away from royal duties last year after an interview he gave to the BBC about his relationship with Epstein.
Epstein took his own life in a US jail cell in August, aged 66, while awaiting trial on sex trafficking and conspiracy charges.
The duke has been heavily scrutinised for his friendship with Epstein, but he has said he did not witness any suspicious behaviour during visits to the US financier's homes.
Mr Berman, the US attorney for the Southern District of New York, has criticised the duke in the past. In January he accused him of providing "zero co-operation" and in March he said Prince Andrew had "completely shut the door" on helping investigators.
On Monday, the duke's lawyers responded for the first time and hit back at the claims as "inaccurate".
Mr Berman then issued a statement, deepening the row. He said: "Today, Prince Andrew yet again sought to falsely portray himself to the public as eager and willing to co-operate with an ongoing federal criminal investigation into sex trafficking and related offences committed by Jeffrey Epstein and his associates."
He said the duke "has not given an interview to federal authorities, has repeatedly declined our request to schedule such an interview, and nearly four months ago informed us unequivocally - through the very same counsel who issued today's release - that he would not come in for such an interview".
"If Prince Andrew is, in fact, serious about co-operating with the ongoing federal investigation, our doors remain open, and we await word of when we should expect him."
The duke's lawyers declined to comment further. But a source said: "This is the third time Berman has breached his own confidentiality rules, further diminishing our trust in the DoJ's willingness to play a straight bat. It's frankly bewildering."
Earlier, the legal team said: "As the public record indicates the DoJ has been actively investigating Mr Epstein and other targets for more than 16 years, yet the first time they requested the duke's help was on 2 January 2020.
"Importantly, the DoJ advised us that the duke is not and has never been a 'target' of their criminal investigations into Epstein and that they sought his confidential, voluntary co-operation."
Lawyer Gloria Allred, who represents some of Epstein's victims, told BBC Breakfast she thinks Prince Andrew has "very little credibility".
"I have a lot of suspicion about what he is saying through his representatives," she said, adding that she did not feel the same way towards Mr Berman.
She added that the victims are in pain and "deserve the truth".
"Questioning the motives of the prosecutors, I just think that's meaningless in this situation," she said.
"Let him step up to the bar of justice, take the oath and just tell the truth."
The duke's lawyers said they had asked US prosecutors to confirm the cooperation would remain confidential, adding: "We were given an unequivocal assurance that our discussions and the interview process would remain confidential."
They added: "The Duke of York has on at least three occasions this year offered his assistance as a witness to the DoJ.
"Unfortunately, the DoJ has reacted to the first two offers by breaching their own confidentiality rules and claiming that the duke has offered zero co-operation. In doing so, they are perhaps seeking publicity rather than accepting the assistance proffered."
The legal team added: "It is a matter of regret that the DoJ has seen fit to breach its own rules of confidentiality, not least as they are designed to encourage witness co-operation.
"Far from our client acting above the law, as has been implied by press briefings in the US, he is being treated by a lower standard than might reasonably be expected for any other citizen. Further, those same breaches of confidentiality by the DoJ have given the global media - and, therefore, the worldwide audience - an entirely misleading account of our discussions with them."
The DoJ has made a formal request to speak to the prince as part of its Epstein inquiry, by submitting a mutual legal assistance (MLA) request to the UK Home Office.
Under the terms of a MLA request if Prince Andrew does not voluntarily respond, he can be called to a UK court to answer questions.
The duke's lawyers described the request as "disappointing" because the Duke of York was "not a target of the DoJ investigation and has recently repeated his willingness to provide a witness statement".
The charges against Jeffrey Epstein
Allegations against Jeffrey Epstein started surfacing in 2005 when the parents of a 14-year-old girl told police in Florida that Epstein had molested their daughter at his Palm Beach home.
The financier was accused of paying girls under the age of 18 to perform sex acts at his Manhattan and Florida mansions between 2002 and 2005.
However, a controversial secret plea deal in 2008 saw him plead guilty to a lesser charge of soliciting a minor for prostitution.
He received an 18-month prison sentence and was released on probation after 13 months.
In July 2019 he was charged in New York with further allegations of sex trafficking and conspiracy and was due to face trial. He pleaded not guilty to all the charges.
In his interview with the BBC's Newsnight programme in November 2019, the duke said he did not regret his friendship with Epstein - which led to Epstein attending events at Windsor Castle and Sandringham - because it had "some seriously beneficial outcomes".
However, he admitted it was wrong of him to visit Epstein at his home in 2010, after his conviction.
He also denied having sex with Virginia Giuffre, when she was a teenager, who said she was trafficked by Epstein when she was 17 and forced to have sex with Prince Andrew.
The duke emphatically denies any form of sexual contact or relationship with her and says any claim to the contrary is false and without foundation.
He said he has no recollection of ever meeting the woman, who was previously known as Virginia Roberts.
Shortly after the interview was broadcast, Prince Andrew said he was "willing to help any appropriate law enforcement agency".
Breach of charity rules
Meanwhile, the Charity Commission has ruled that Prince Andrew's trust, which supported his charitable work, was in breach of rules over payments of more than £355,000 to a former trustee.
The duke's charitable body allowed the former trustee, who was an employee of Prince Andrew's household, to work as a director for a fee for three of its subsidiary companies - in breach of charity law.
The duke's household was then reimbursed £355,297 for a proportion of this employee's time by the subsidiaries, the Charity Commission said in a statement on Tuesday.
"Trustees cannot be paid to act as directors of a subsidiary company, unless there is authority from the charity's governing document or the payments are authorised by the Commission or the court, none of which were in place at the charity," the statement read.
His household has since paid back the money to the Prince Andrew Charitable Trust (PACT).
The trust has also notified the commission of its intention to wind up, with the remaining funds being distributed to other charities.
A statement from the current trustees said former trustees who were in post at the time had "inadvertently breached charity law".
"The current trustees of PACT are grateful to the Charity Commission for its support in bringing this matter to a satisfactory conclusion with the payment of funds by HRH The Duke of York's office to the Trust," the statement said.