Downing Street has defied calls to remove Keir Starmer’s most senior aide, insisting Morgan McSweeney retains the prime minister’s confidence, as frustration grows over a wait for documents on Peter Mandelson, which some fear could last for weeks.

Amid warnings from Labour backbenchers that McSweeney’s survival would leave Starmer’s position “untenable”, Starmer apologised to victims of Jeffrey Epstein for appointing Mandelson, a close friend of the convicted child sex offender, as US ambassador.

A day after a chaotic Commons deal to release vetting papers over Mandelson’s appointment left many Labour MPs mutinous, there was still fury about the role of McSweeney, the PM’s chief of staff.

One Labour MP said: “People want [McSweeney] to go, more than ever before. The current situation is unsustainable.”

Karl Turner, the Hull East MP and a vocal critic of the current No 10 operation, said McSweeney staying would leave the prime minister’s position “untenable”. “I don’t want the PM to go. What I want is the PM to make changes,” he told the BBC.

Downing Street officials pointed to Starmer’s strong defence of McSweeney in the Commons on Wednesday, in which he said nothing had changed. Supporters of the PM are aware that shedding his chief of staff could leave Starmer more directly in the firing line in a future crisis.

Amid continued speculation about a possible leadership challenge, Starmer sought to regain the initiative with a speech and media Q&A in Hastings, ostensibly about community values but which was dominated by the Mandelson aftermath.

Starmer said he understood the frustration of his MPs, and called on them to rally round the government.

Saying the victims of Epstein had “lived with trauma that most of us could barely comprehend”, Starmer went on: “I want to say this. I am sorry – sorry for what was done to you, sorry that so many people with power failed, sorry for having believed Mandelson’s lies and appointed him, and sorry that even now you’re forced to watch this story unfold in public once again.”

Pressed on why he had approved the appointment when Mandelson’s post-prison links to Epstein were public knowledge, he dodged the question, blaming what he said were lies by Mandelson and the need to examine vetting procedures.

There is increasing frustration among some ministers about the delay in releasing the documents. None are expected until next week at the earliest, and with officials saying they do not even know how many messages and files might be involved, there are concerns the process could take weeks.

Starmer had planned to release documents on Wednesday, before the Conservative motion that forced the issue, but he was delayed by a warning from the Metropolitan police that some of the information could affect their investigation into whether Mandelson leaked market-sensitive information as a minister.

Some in the cabinet believe the government should overrule the police, with one arguing it would show “leadership” to exercise judgment that documents relating to Mandelson’s vetting were not likely to have any links to the criminal investigation.

However, of the material the Met has so far been shown by the government, it is understood to have concerns over only a small number of documents being published, believed to be fewer than 10, a small portion of those reviewed by detectives.

For the majority of documents, detectives raised no objections to them being released to the public.

Wednesday’s Commons motion said any decisions on whether documents should be held back or redacted would be made not by the government but by parliament’s intelligence and security committee (ISC), a compromise that got Labour backbenchers on board.

In a letter to Starmer on Thursday, the chair and deputy chair of the ISC said any material deemed sensitive should be provided in full to them, with the committee deciding what should not be published.

The ISC could not say how long its task would take until it knew the number of documents to be examined, said the letter from Labour peer Kevan Jones, the chair, and Conservative MP Jeremy Wright, the vice-chair. The committee, they added, would be “grateful to, now, be told the date on which we will receive those papers”.

While Downing Street said it had “begun discussions with the ISC about the process for releasing these documents”, the committee disputes this, saying it was carrying out the wishes of the Commons, not No 10, and that ministers simply had to provide the information.

The vacuum of new information is making it harder for Downing Street to move on from speculation about Starmer’s future. UK long-term borrowing costs hit their highest level since the budget on Thursday as traders reacted to the possibility of a change in No 10.

Asked about mass dissatisfaction among his MPs, Starmer told them to instead focus on key messages like the cost of living, saying: “Every minute you spend not talking and focusing on that is an absolute minute wasted.”

But even many sympathetic voices seem to be losing patience. Speaking to Sky’s Electoral Dysfunction podcast, Harriet Harman, the former Labour deputy leader, said Starmer should “stop blaming Mandelson”, take responsibility for the appointment and undertake a “reset” of his No 10 team.

She added: “I don’t think it’s inevitable that it will bring him down, but it will bring him down unless he takes the action, which is really necessary for him to take.”

Opposition parties have called for a no-confidence vote in the prime minister, with the Tory leader, Kemi Badenoch, and the Liberal Democrat leader, Ed Davey, raising the issue on Thursday.