Thames Valley Police issued the statement as it updated reporters on its investigation into allegations of misconduct in public office by the former prince, now known as Andrew Mountbatten-Windsor.
The force covers the area west of London where Mountbatten-Windsor lived for many years.
Mountbatten-Windsor was arrested on February 19 and held for hours as police questioned him about the allegations, linked to his friendship with the late convicted sex offender Jeffrey Epstein.
The arrest was an extraordinary move in a country where authorities once sought to shield the royal family from embarrassment.
Mountbatten-Windsor has repeatedly denied wrongdoing.
Police previously said they were assessing reports that Mountbatten-Windsor sent trade reports to Epstein in 2010 when the then-prince was Britain's special envoy for international trade.
Those reports were based on correspondence between the two men that became public when the US Justice Department released millions of pages of documents from its investigation into Epstein.
But detectives renewed their appeal for witnesses amid concern that the public believes they are only investigating allegations linked to the trade reports, when in fact misconduct in public office can apply to a much broader list of offences, Britain's Press Association reported.
"Misconduct in public office is a crime that can take different forms, making this a complex investigation,'' Assistant Chief Constable Oliver Wright said on Friday.
"Our team of very experienced detectives are working meticulously through a significant amount of information that has come in from the public and other sources."
Misconduct in public office can include sharing confidential financial information, financial misconduct, wilful neglect of duty, and sexual misconduct.
It also covers corruption and improper interference, conflict of interest, perverting the course of justice, dishonesty or fraudulent conduct or misconduct leading to personal gain.
Police said they were looking into "a number of aspects of alleged misconduct" following the release of the US documents, and they were working with the Justice Department to get additional information related to the investigation.
Thames Valley Police also issued an update on its inquiry into allegations that a woman was taken to a location in Windsor for sexual purposes in 2010.
"Should she wish to report this to police it will be taken seriously and handled with care, sensitivity and respect for her privacy,'' police said in a statement.
Florida lawyer Brad Edwards told the BBC in January that he represented a woman who said Epstein sent her to England in 2010 to have a sexual encounter with Mountbatten-Windsor at his home in Windsor.
King Charles III stripped his younger brother of his royal titles in late 2025 as he sought to distance the royal family from the fallout from the Epstein scandal.
Those files showed how the wealthy financier used an international web of rich, powerful friends to gain influence and sexually exploit young women and girls.
Nine police forces in the UK say they are investigating potential wrongdoing related to Epstein.
Britain's former ambassador to the US Peter Mandelson was fired in 2025 after documents revealed that he had a longer and deeper relationship with Epstein than he previously acknowledged.
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