Sir Keir Starmer believes that Peter Mandelson should not be a member of the House of Lords or use the title, Downing Street has said.
While the prime minister does not have the power to remove life peerages himself, he is calling on the House of Lords to update its disciplinary procedures to create a process for that to happen.
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The prime minister's official spokesman said: "The prime minister believes that Mandelson should not be a member of the House of Lords or use the title.
"The prime minister doesn't have power to remove [his peerage], and is calling on the Lords to modernise its disciplinary procedures for those bringing the House into disrepute."
The last time peerages were removed was in 1917 when legislation was introduced to remove them from "enemies" of the UK during the First World War, and set out a process for doing so - although it was limited to just that period.
The government, which has previously said that an act of parliament is the only way to strip someone of a peerage, is not currently planning on introducing such legislation, but is calling on the House of Lords to work with them in "strengthening the circumstances in which disgraced members can be removed".
Asked if Lord Mandelson should testify before the US Congress about Epstein, Sir Keir's spokesman said: "The prime minister has said victims have to be the first priority, so yes, if he has information in that regard, he should be prepared to share it however he can."
The prime minister has also asked the cabinet secretary - the UK's most senior civil servant - to "urgently" review all available information on contact between the former minister and Epstein after emails appeared to show conversations between the pair about government and political matters.
Why are there calls for Mandelson to lose his peerage?
The demand for Lord Mandelson to be stripped of his peerage comes after documents in newly released files relating to the paedophile financier appeared to show that Lord Mandelson received $75,000 from him.
The latest batch of files released by the US Department of Justice includes three apparent bank statements detailing three money transfers of $25,000 each from Epstein to the former New Labour grandee in 2003 and 2004 - while he was the MP for Hartlepool.
It is unclear whether the payments ever made it into any named accounts.
Lord Mandelson, who was the Labour MP for Hartlepool when the files suggest the payments were alleged to have been made, resigned his membership of the party on Sunday night.
The peer, who has denied any record or recollection of the payments and questioned their authenticity, said in a statement he wanted "to repeat my apology to the women and girls whose voices should have been heard long before now".
He added: "I was wrong to believe Epstein following his conviction and to continue my association with him afterwards. I apologise unequivocally for doing so to the women and girls who suffered".
The New Labour grandee, who was sacked as the UK's ambassador to the United States over his links to Epstein, appeared in a picture found in the files wearing only his underwear and a t-shirt, which Sky News has confirmed was taken in the paedophile's Paris flat.
A spokesperson for Lord Mandelson previously told Sky News: "No one can say who or where the photo was taken. Lord Mandelson has absolutely no idea or indeed whether it has any connection to Epstein at all."
Opposition demands investigation into appointment
The leader of the Conservative Party has demanded a "full Cabinet Office investigation" into the process that led to Lord Mandelson being appointed ambassador last year, from which he was sacked in September after it emerged he had continued his relationship with Epstein following the paedophile's conviction in 2008.
Kemi Badenoch told broadcasters: "We need to understand how it came to be that Peter Mandelson was appointed as ambassador in the first place.
"It does not appear that there was proper vetting - allowing special advisers to carry out vetting is not the right process. Why was this waived? This is the heart of the scandal.
"Why was it that Keir Starmer, despite knowing the allegations surrounding Peter Mandelson, insisted on making him the British ambassador, waving away processes which were in place? That's why we want to see a full investigation into."
The leader of the Liberal Democrats has called for the government to introduce the necessary legislation to strip Lord Mandelson of his peerage, saying it is "the very least they can do for the victims and survivors of his friend Jeffrey Epstein"
Sir Ed Davey added: "If Mandelson has any shame left he will retire from the House of Lords today while this process gets underway."