Mandelson quit the Labour Party on Sunday to prevent "further embarrassment", after he was fired from his envoy role last year over revelations about his connections to the late convicted sex offender.
He said he had no recollection of any payments after the files appeared to show he had received donations of $US25,000 ($A35,995) from Epstein. The Financial Times said he received $US75,000 ($A108,000) in total.
Prime Minister Keir Starmer said Mandelson should be removed from parliament's upper chamber.
Separately, the British police said they were reviewing "a number of reports" of alleged misconduct in a public office to determine if they meet the threshold for a criminal investigation.
Among the latest batch of documents released by the US Justice Department, an email suggested Mandelson had shared a confidential government briefing with the financier.
The memo from an adviser to then-prime minister Gordon Brown, which was copied to Mandelson and others, discussed economic policy, including a recommendation that they should consider the sale of non-strategic assets to bring down debt.
Mandelson forwarded the email to Epstein saying "interesting note that's gone to the PM", with Epstein replying: "What saleable assets?"
Opposition politicians called on the police to investigate whether Mandelson, a minister in Labour's 1997-2010 governments of Tony Blair and Gordon Brown, had breached confidentiality rules.
Britain's Metropolitan Police did not respond to a Reuters request asking whether they were considering opening an investigation.
Mandelson said in a letter to the Labour Party that he was sorry to be linked once again to the "understandable furore surrounding Jeffrey Epstein".
But he said he believed that allegations about financial payments to him by Epstein were false and he would investigate.
Starmer's spokesperson said on Monday Mandelson should not be a member of the House of Lords but added that the prime minister did not have the power to remove him.
"He (Starmer) is calling on those in the Lords to work with the government to modernise disciplinary procedures in the House to allow for the easier removal of Lords who have brought the House into disrepute," the spokesperson said, adding that Starmer had instructed the cabinet secretary to review all available information regarding Mandelson's contacts with Epstein.
Mandelson could choose to retire from the House of Lords but ousting him would require the government to pass legislation. He is currently on a leave of absence.
During the late 1990s, Mandelson, who was photographed in his underwear in the new Epstein files, played a central role in Labour's electoral success as Blair became prime minister.
Mandelson, also a former European Union trade commissioner, came under scrutiny last year when US lawmakers released documents including a letter in which he called Epstein "my best pal", leading to his dismissal as Britain's ambassador.
Separately, Starmer said the former prince Andrew should testify before a US congressional committee following new revelations about his links to Epstein.
