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 - and that of another potential challenger Wes Streeting - have said they will not be giving any media interviews over the wekend, 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."

Asked if he would 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 and 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 and 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 previously said that 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.

The scale of Burnham's victory in Makerfield, where he increased Labour's share of the vote by 10% and 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 and he has the weekend".

"I think he needs the peace and 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 ministers have rallied round Sir Keir, with Chris Ward telling the BBC's Politics Live: "The Prime Minister has a mandate from the party to be the leader, and from the country to lead the country.

"That's the mandate he's been delivering for the last two years.

"And he's going to step up delivering in the coming months as we move into the next phase of the government."

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.

Conservative leader Kemi Badenoch accused Labour of being "obsessed" with "drama".

She was speaking from Aberdeen South, where her party had won its first by-election in Scotland in more than 50 years.