Sir Keir Starmer believes Lord Mandelson should no longer be a member of the House of Lords or use his title, a Downing Street spokesperson has said.
However, the spokesperson said the prime minister does not have the power to remove his title, and has called on the Lords to modernise its disciplinary procedures for those bringing the house into disrepute.
Lord Mandelson last night resigned from the Labour Party, saying he did not want to cause the party "further embarrassment" due to continued revelations over his links to the disgraced paedophile financier Jeffrey Epstein.
The Conservative Party has called for a "full investigation" into Lord Mandelson's links with Epstein and his appointment as UK ambassador to the US.
While both the Tories and the Liberal Democrats have called on Lord Mandelson to be stripped of his peerage.
Lord Mandelson most recently served as UK ambassador to the US, but was sacked by Sir Keir Starmer in September.
He previously served as Northern Ireland secretary, business secretary, and de-facto deputy prime minister in the governments of Tony Blair and Gordon Brown.
The last time peerages were removed was in the early 1900s 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.