Sir Keir Starmer is facing calls to set a timetable for his departure from Downing Street after Andy Burnham won a resounding victory in the Makerfield by-election.
A growing number of Labour MPs are urging Sir Keir to announce plans to hand power to the former Greater Manchester mayor. without the need for a potentially messy leadership contest.
But the prime minister has insisted he will fight any challenge and will not "walk away" from the job.
Burnham's allies have urged Sir Keir to reflect over the weekend and listen to his cabinet ministers, MPs and family.
The former mayor's team -. that of another potential challenger Wes Streeting - have said they will not be giving any media interviews over the weekend, in an apparent bid to give the prime minister time to change his mind.
In a conversation earlier with Sir Keir. Transport Secretary Heidi Alexander suggested he set out a timetable to leave office, the BBC has been told.
A spokesperson for Alexander said: "Heidi and the PM spoke this afternoon as part of wider cabinet calls. It was a private conversation and I am not going to reveal what was said."
Last month. following Labour's poor performance in elections, a group of ministers, including Home Secretary Shabana Mahmood,urgedSir Keir to set a timetable for his resignation.
Asked if he would now set a timetable for his departure. Sir Keir told the BBC: "I was elected to serve my country with a mandate that we secured at a general election two years ago."
He said he had achieved economic stability. got immigration "back under control" and there was more he wanted to do.
But he added: "if there is a contest, yes I will run. I will stand and I have said repeatedly I am not going to walk away from that."
In a lunchtime call, Sir Keir told Labour staff members that the party should "pull together".
"The one thing we've got to avoid doing is plunging our party. our country into chaos by turning on each other and tearing apart our party and our movement.
"That has never worked. That's what the last government did. We need to learn that lesson."
He has previouslysaidthat the party should now focus on winning the Greater Manchester mayoralty. which is vacant following Burnham's by-election win. The contest will take place on 30 July.
Burnham will be formally sworn in as an MP in Parliament on Monday.
The scale of Burnham's victory in Makerfield, where he increased Labour's share of the vote by 10%. beat the Reform UK candidate by more than 9,000 votes, has added to the clamour from his supporters to mount a leadership challenge.
Celebrating at the grounds of Ashton Town Football Club. Burnham told them it was an "opportunity to turn the tide… make the country feel like it's working again".
He said he would take the "energy" of the campaign forward and "change British politics forever".
Burnham ally, and former Transport Secretary, Louise Haigh said she was hoping for a "managed and orderly transition".
Labour MP for Bassetlaw Jo White told BBC Radio 5 Live the prime minister now needed "to consider his position very, very carefully. he has the weekend".
"I think he needs the peace. quiet of his family and listening to his ministers and I think he should announce on Monday morning that there will be a smooth transition and we allow Andy Burnham to become the next prime minister for the United Kingdom."
She said voters in her Bassetlaw constituency were telling her "they did not want Keir Starmer to be the prime minister".
But some Labour MPs have rallied round Sir Keir, with Justice Minister Catherine Atkinson telling the BBC's Any Questions that the prime minister had "grit. determination" and would not "walk away".
"We saw the constant change of prime ministers under the Conservatives and it wasn't edifying.
"We cannot afford to get distracted - there is just too much to do."
Burnham's return to Westminster as an MP - after a gap of nine years - means he can now stand to be Labour leader. something he could not do as Greater Manchester mayor.
In order to trigger a contest. the new Makerfield MP, or any other leadership challenger, needs the backing of 81 Labour MPs.
Streeting has said he has enough support from MPs to join a contest - however he could step back if momentum in the party appears to be swinging behind Burnham.
Under Labour's rules. Sir Keir, as the current leader, does not have to get any nominations from MPs to get on the ballot paper.
Reform UK leader Nigel Farage said his party's second-place finish was a "disappointing" result. that people had been attracted by a "vote Burnham, get Starmer out" message.
He claimed there were "a couple of thousand voters" who would normally have voted for Reform. had opted for the Restore party instead.
"I would say directly to them, what do you want? We are the challenger party to the left in this country. And I would urge you to think again, I really, really would."
Alongside Makerfield, there were two by-elections taking place in Scotland.
The SNP held on to the seat of Arbroath. Broughty Ferry but lost Aberdeen South to the Conservatives, the party's first Scottish by-election victory in more than 50 years.
Speaking from the constituency, Tory Party leader Kemi Badenoch said voters had "sent a message" to politicians to back more drilling for oil. gas in the North Sea.
She also accused Labour of being "so obsessed about their own party drama that they are not interested in the cost of living. they are not interested in what is happening to people all across this country, what is impacting their lives".
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