Buckingham Palace says it will support police if contacted over allegations about Andrew Mountbatten-Windsor.
The palace also said King Charles had "profound concern" over claims about his brother, in a statement released following revelations in the Epstein files.
Thames Valley Police has said it is assessing claims that Andrew shared confidential documents with the late convicted sex offender Jeffrey Epstein, while the former duke served as UK trade envoy.
Andrew denies any wrongdoing in relation to Epstein.
Follow latest updates on the Epstein files
A palace spokesperson said: "The King has made clear, in words and through unprecedented actions, his profound concern at allegations which continue to come to light in respect of Mr Mountbatten-Windsor's conduct.
"While the specific claims in question are for Mr Mountbatten-Windsor to address, if we are approached by Thames Valley Police we stand ready to support them as you would expect.
"As was previously stated, Their Majesties' thoughts and sympathies have been, and remain with, the victims of any and all forms of abuse."
Sky News royal correspondent Rhiannon Mills said it was an "extraordinary" statement to put out while Prince William was on a diplomatic trip to Saudi Arabia.
Mills said: "The fact it has also come as Prince William embarks on a hugely important trip on behalf of the UK government, trying to cement relationships here in Saudi Arabia, in itself says so much about this statement.
"When royals are on tour, nothing is done to distract from the important business they're doing on behalf of the UK government, and the fact that Buckingham Palace has now felt the need to put out another statement regarding Andrew, responding for the first time to the latest release of the Epstein files, is absolutely extraordinary."
She added: "In the past, I think they would have tried to ignore this, but the amount of detail and information that has been exposed in these recent Epstein files means that they simply cannot ignore it."
Earlier, the Prince and Princess of Wales publicly addressed the Epstein scandal for the first time, with Kensington Palace saying they were "deeply concerned" at the "continued revelations" and that their thoughts "remain focused on the victims".
The palace statement came after the King was heckled for the second time in a week about Andrew.
He arrived at Clitheroe train station on Monday to greet crowds at the start of an awayday to Lancashire, when a man shouted: "How long have you known about Andrew?"
The rest of the crowd booed after the question was asked.
Earlier on Monday, Ghislaine Maxwell, the former girlfriend of Epstein, stayed silent during a behind-closed-doors session of the US House Oversight Committee's investigation into the paedophile financier.
Maxwell, 64, is serving a 20-year prison sentence for her role in helping Epstein sexually abuse teenage girls.
She refused to answer questions, citing her 5th Amendment rights under the US constitution, which includes the right to remain silent.
(c) Sky News 2026: King has 'profound concern' over Andrew claims - and Buckingham Palace 'ready to support' police if contacted

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