Mandelson, 72, was dismissed last year as the UK's ambassador to the US when it emerged that he had contact with Epstein after his sex trafficking conviction in 2008.
Now new emails have been exposed in which he appears to discuss political issues. Among other things, he is said to have informed Epstein in advance of a bailout package for the euro in 2010, according to Sky News.
In addition, documents suggest that in 2003-2004, when he was an MP, he received a total of $75,000 (about SEK 670,000) from Epstein. Mandelson told the BBC on Sunday that he had no memory of the transfers.
British police announced on Tuesday that a criminal investigation into misconduct had been launched.
Mandelson has left the Labour Party and his seat in the House of Lords, but retains the title of Lord - it can only be taken away from him by a decision in Parliament.
Prime Minister Keir Starmer said at a cabinet meeting on Tuesday that Mandelson had "let his country down", according to the British leader's office.
Mandelson laid the foundations for "New Labour" together with Tony Blair and Gordon Brown, which led to Blair's landslide victory in 1997.
