Yvette Cooper has appeared to blame No 10 and the Cabinet Office for appointing Lord Mandelson to the Washington ambassador post.
The Foreign Secretary clarified on Tuesday that her department had not been involved in checking Lord Mandelson's appropriateness for the role before it was announced.
In a letter to the Commons foreign affairs committee Ms Cooper and Sir Oliver said: "The Propriety and Ethics Team in the Cabinet Office (PET) conducted a due diligence process, prior to the announcement of Peter Mandelson's appointment on 20 December 2024 at the request of No 10.
"The FCDO was not asked to contribute to that process and no issues were raised with the FCDO as a result of this process. This was not a security check.
"After Peter Mandelson's appointment was announced, [the FCDO] started the ambassadorial appointment process, including National Security Vetting, in advance of him taking up his post."
Formal security vetting, which focuses on blackmail risk and was overseen by the Foreign Office (FCDO), was only carried out after the appointment was made public.
Sir Keir Starmer and Morgan McSweeney, his chief of staff, made the Labour grandee the UK ambassador to the US late last year.
But the Prime Minister was forced to sack Lord Mandelson when previously unknown emails revealed the ex-US ambassador to the UK urged Jeffrey Epstein to fight for early release from prison after he was found guilty of child sex offences.
Dame Emily Thornberry, the chairman of the Commons foreign affairs committee, had written to the Foreign Office posing a series of questions about Lord Mandelson's vetting.
Ms Cooper and Sir Oliver responded by setting out the Foreign Office's role in what amounted to a two-step process.
It was the the Cabinet Office that reportedly offered up a two-page summary of Lord Mandelson's known friendship with Epstein before the appointment.
Tory leader Kemi Badenoch accused Sir Keir of "hiding from Parliament" because he was not present for the emergency debate on Lord Mandelson's sacking on Tuesday.
Conservative former minister Sir David Davis argued there are double standards applied to those of "Labour royalty", with Lord Mandelson retaining the Labour whip.
The debate came ahead of US President Donald Trump's state visit to the UK, which Conservative leader Mrs Badenoch said risks being overshadowed by scandal.
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