Sir Keir Starmer has warned Andy Burnham against launching an immediate challenge to his leadership if he becomes an MP, urging him, and the party, to focus instead on the election for a new Greater Manchester mayor.
If Burnham wins in Makerfield on Thursday he would have to resign as Manchester mayor, with a by-election to replace him expected by 6 August.
Burnham is widely anticipated to challenge the prime minister for the leadership, if he is elected to Parliament.
Speaking from the G7 summit, the prime minister said a leadership contest would be a "bad thing" for the country and reiterated that he intended to fight any challenge.
Sir Keir said the potential mayoral election would be "very important" and that his party were "going to have to pull our sleeves up to make sure that there is another Labour victory".
The prime minister also indicated that he would offer Burnham a cabinet job if he wins in Makerfield, telling reporters: "I hope he wins the by-election and he'll play a big part in the Labour government."
The prime minister's warning comes as Labour MP Wes Streeting says he is prepared to trigger a leadership contest as soon as next week.
Streeting resigned as health secretary last month but has said he delayed making a leadership challenge until after the Makerfield by-election to give Burnham a chance to take part.
Speaking to BBC's Newsnight, Streeting said "uncertainty and paralysis" in the Labour leadership would have to be resolved if the party wins Thursday's Makerfield by-election.
Asked about Streeting's threat, Sir Keir said: "There is Westminster talk about what might happen in by-elections.
"Meanwhile, I would just gently point out, that we do have a Manchester mayoralty by-election which will follow immediately on if Andy Burnham wins the by-election.
"I hope he wins, but we then tip straight into the Manchester mayoralty by-election… so we're all going to have to focus on that."
The prime minister's comments are a preview of the argument he is likely to make on Friday should Burnham win in Makerfield.
Some Labour MPs fear that Reform UK could win the Manchester mayoral by-election, even though when it was last contested in 2024 Burnham won by a vast margin.
Burnham's supporters say that the importance of the mayoralty only strengthens the case for him to become prime minister sooner rather than later.
Reflecting on his leadership more widely, Sir Keir said being prime minister "is the privilege of my life, and every day I remind myself that that is an honour.
"It is a duty, and I'm here to serve, that is why I came into politics.
"Not a day goes by where I don't remind myself it's a privilege."
Asked if, in the event of a leadership contest, ministers would have to resign if they wanted to back one of the prime minister's rivals, Sir Keir said he would not "start getting involved in hypotheticals".
Sir Keir's leadership was further destabilised last week when John Healey and Al Carns resigned as the defence secretary and defence minister in a row over funding.
On Tuesday, the chief of the defence staff warned that the UK's armed forces would have to "dial back" training and operations if they did not receive more money than is currently being offered.
Sir Keir said the new Defence Secretary Dan Jarvis was "looking at what his priorities and capabilities are" adding: "I think the chief of the defence staff made it clear that those discussions were ongoing."
A full list of the candidates standing in the Makerfield by-election can be found here.
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