It is a "personal decision" for Sir Keir Starmer whether he chooses to fight any potential leadership contest, Culture Secretary Lisa Nandy has said.
She told the BBC's Sunday with Laura Kuenssberg that Sir Keir had "shown before that he's up for a fight" and "I wouldn't write off the prime minister".
The PM has defied calls to step down in recent days, after nearly 90 of his own MPs urged him to go and five ministers resigned.
Nandy also voiced her support for Andy Burnham to be "back in Parliament at the heart of power". The Greater Manchester mayor is seeking to stand for Labour in the Makerfield by-election and is widely expected to launch a leadership challenge if he wins.
On Saturday Wes Streeting confirmed he would stand in any future leadership race, after he resigned as health secretary earlier this week.
Sir Keir would automatically be on the ballot paper if he chose to contest any leadership election, and the prime minister has said he would stand if one took place.
Asked if she thought Sir Keir should be replaced as Labour leader, Nandy - who represents the Greater Manchester constituency of Wigan and is an ally of Burnham - told the BBC: "No I don't. If I did I wouldn't be in his cabinet."
"I think that we were elected to bring an end to the chaos," she said.
Pressed over whether she thought Sir Keir should run in any leadership contest, the culture secretary said: "He said himself that he will."
She added: "It's a very personal decision for him.
"I haven't spoken to him this weekend but I've spoken to him several times over the last week and obviously he's shown before that he's up for a fight."
She pointed to Sir Keir's landslide general election victory in 2024, after sceptics said he would not be able to return Labour to power in just one term.
But Nandy said last week's disastrous set of election results for Labour showed "people feel they haven't seen enough fight from us".
She added: "We have fought for people but the message is loud and clear, they want to see us on the pitch fighting harder, speaking louder and doing more."
Nandy, who was out campaigning alongside Burnham in Makerfield on Saturday, said: "We were hearing that loud and clear.
"People want that and they want voices from our part of the country and from all of those parts of the country that have been written off for too long to be heard much louder and clearer at the heart of government."
Nandy – who ran against Sir Keir to become Labour leader in 2020 - ruled out standing in any future contest herself.
On Friday, Labour's ruling National Executive Committee, which had blocked Burnham's previous attempt to stand in a by-election in January, cleared him to seek selection as Labour's candidate in Makerfield.
It came after Labour MP Josh Simons said he would resign to make way for Burnham, while Sir Keir's allies indicated the prime minister would not seek to block his return to Parliament.
Nandy admitted it would be a "tough fight" for Burnham to win in Makerfield, with Reform UK performing strongly in last week's council elections in the area.
Labour won the constituency with a majority of 5,399 votes in the 2024 general election, but Nigel Farage's party has been consistently leading in national opinion polls since spring last year.
There are no precise figures for how the parties performed in Makerfield during the local elections because the ward boundaries do not fully align with the constituency boundaries - but Reform UK won roughly 50% of the vote share in the area.
However, Burnham's backers argue this does not account for the strong personal support he has in Greater Manchester, where he has won three successive landslides in mayoral elections.
Nandy said: "Because of Andy's record as mayor, people who didn't vote for [Labour] last week were saying that they would vote for us again."
She added: "That's why I make no apology for saying that I think he is a really important voice that needs to be heard loud and clear at the centre of Westminster."
Simons told the programme it would be "existential" for the Labour Party if it lost the Makerfield by-election.
He said the contest was "about a fundamental question for my party, which is can they win back the trust of working-class people".
"If the answer to that question is yes, then I think we can get to a moment of unifying and coming together from the different traditions across my party," he added.
However, Conservative leader Kemi Badenoch said: "It doesn't matter whether it's Andy Burnham or Keir Starmer, the problem is the Labour Party."
The UK's relationship with the European Union looks set to become an issue in any future leadership contest.
In a speech on Saturday, Streeting said leaving the EU had been a "catastrophic mistake" and the UK should "one day" rejoin the bloc.
Burnham has also said there may be a case for rejoining the EU "in the long-term", but insisted he was "not advocating that in this by-election".
Asked about Streeting's comments, Nandy said that while she campaigned for Remain in the 2016 referendum, "if the answer to all of this was the European Union, then essentially we'd be saying to people what was going on in 2015 in towns like Wigan was absolutely fine".
"Well, I can tell you that it wasn't, that people's living standards had been falling, people's high streets had been falling apart, people's kids had had to get out to get on for some time, and that's to do with deindustrialisation and the failure of governments to address it," she said.
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