Labour MPs issued further calls on Friday for Starmer to dismiss his chief of staff Morgan McSweeney, whom they blame for Mandelson's appointment as US ambassador despite the peer's links to pedophile financier Jeffrey Epstein.
Backbencher Simon Opher called for a "clear out at Number 10," telling the BBC: "If my chief of staff had done this, I think he would be looking for another job."
Others calling for McSweeney's departure include veteran MP Clive Efford and Southport's Patrick Hurley, who suggested another job should be found for him running the party's campaigns rather than the government.
Their comments follow an intervention by Labour's former deputy leader Baroness Harriet Harman, who said Starmer should consider "a real reset" in Downing Street and warned his premiership could be finished if he does not take the right course of action.
But other than a handful of backbenchers, most MPs have so far declined to call for the prime minister himself to go, stressing their support for Starmer while urging a change in backroom staff.
The prime minister's official spokesman has said Starmer retains "full confidence" in McSweeney.
In a speech on Thursday, Sir Keir defended his handling of the Mandelson affair, accusing the peer of lying during his vetting for the US ambassador job and offering an apology to Epstein's victims for believing his "lies".
He also insisted "none of us knew the depth of the darkness" of Mandelson's relationship with Epstein when he was appointed.
The extent of what was known about the relationship is expected to be revealed when documents relating to Mandelson's appointment are published following a motion in parliament demanding their release.
Along with Mandelson's vetting papers, the motion called for the release of other documents including messages between Mandelson and ministers and senior advisers both before and during his time as ambassador.
The files are understood to include thousands of documents.
Starmer believes the files will prove Mandelson lied during his vetting but the publication of communications with ministers and senior officials has the potential to prove embarrassing for the government.
Publication of the full tranche of documents could take some time, as parliament's Intelligence and Security Committee must review any items that the government wishes to withhold for national security reasons.
The committee has yet to set out a timetable for making its decisions on what can be released.
The Metropolitan Police has also asked for some documents to be withheld, claiming it could jeopardise its criminal investigation into allegations Mandelson passed on market-sensitive information to Epstein when he was business secretary following the 2008 financial crisis.
The number of documents, and the sensitive nature of some of them, mean the files could be released piecemeal rather than in one large tranche.
Starmer's official spokesman said the government was "committed to transparency" and would comply with the motion to release the documents.
Mandelson has been approached for comment and while he has yet to speak publicly, the BBC said it understood he maintains he did not act criminally and that his actions were not for personal gain.
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