The Prime Minister vowed not to walk away from his post on Friday, in the immediate aftermath of Andy Burnham winning the Makerfield by-election, but pressure has been mounting over the weekend.

The number of Labour MPs calling for Sir Keir to go has since topped 100 – just under a quarter of the party’s MPs – and includes some who signed a letter warning against a leadership contest just last month.

Labour grandees have also spoken out, with former home secretary Alan Johnson saying Sir Keir should step aside and Lord Falconer saying he has “no authority” because it is assumed he will be replaced by Mr Burnham.

Business Secretary Peter Kyle told broadcasters on Sunday he had not spoken to the Prime Minister since Friday, when he had a “frank conversation” with him.

Asked about reports Sir Keir Starmer is planning to announce his resignation as soon as the coming week, he told Sky News’ Sunday Morning with Trevor Phillips: “I have nothing to believe that they are true. I’m seeing a lot of speculation out there.

“The only thing I can say with fact is that the Prime Minister is hard at work, as he is every day.

“He is one of the most hardworking people I’ve ever come across, and today, as in every other day I’ve ever known Keir, he is out there working hard.

“At the same time he is also trying to create the space where he can think and reflect on the political realities and challenges, and the opportunities, that lie before us.” He told the BBC that “whatever unfolds” in the coming days will be a “functional process”.

“I don’t know what’s going to unfold in the days that lie ahead. I don’t know the decisions that he will make on behalf of our country as he considers these issues, and then makes decisions.

“But we will find a way for this to be whatever unfolds, a functional process, one where the Labour Party is seen to put the interests of the country first and foremost, and we will carry on delivering for this country through whatever does unfold in the days ahead,” he told the Sunday with Laura Kuenssberg programme.

No 10 said Sir Keir’s position remained unchanged from Friday, when he said he will not “walk away” from Downing Street and will stand in any potential contest.

But asked if the Prime Minister still plans to fight a leadership challenge, Mr Kyle said “these are decisions for Keir to make” and repeated the PM is “taking the time to think through what the political realities are today compared to last week, the week before”.

Sir Keir warned Labour staffers during a call on Friday lunchtime to avoid “plunging our party and our country into chaos by turning on each other and tearing apart our party and our movement”.

Foreign Secretary Yvette Cooper is among Cabinet ministers reported to have told him he should set out a timetable for his departure.

She declined to comment.

Mr Kyle would not say what his advice to Sir Keir had been when they spoke on Friday.

Asked if he thought Mr Burnham would make a good prime minister, he said: “I think there is lots of people out there that have the qualifications, the temperament and the qualities to become prime minister. I think Andy Burnham could be one of those people.” Mr Burnham is due to make his return to Westminster on Monday to be sworn in as the new MP for Makerfield.

It is understood his camp wants Sir Keir to set out his plans in the coming days but would accept a timetable that kept him in No 10 until September.