Sir Keir Starmer has repeated his insistence that he will "not walk away" from the job of prime minister despite more than a week of turbulence in his party, which saw five of his ministers resign.
He said the last 10 days had seen "a lot of activity which hasn't been as focused as it should have been, and I remind myself every day that I was elected to office to serve the people... and that's what I'll be getting on with".
Sir Keir's leadership is likely to be challenged by Greater Manchester mayor Andy Burnham, if he is successful in his bid to become Labour MP for Makerfield.
Setting out his pitch, Burnham told an investment summit in Leeds that a vote for him was a vote to "change Labour".
He called for a transfer of money and resources from "a bloated national state" to "a malnourished local one", saying the country needed "serious rewiring".
"We have hollowed out councils and have created an unaccountable state, where too much is delivered by outsourced agencies outside local councillors' control."
Burnham said his party's offer to voters had "not been good enough" and that "a vote for me would be a vote to change Labour".
"Labour needs to change if we are to regain people's trust."
Questions about Labour's position on Brexit emerged over the weekend when former health secretary Wes Streeting, Burnham's potential leadership rival, told a conference that the "biggest economic opportunity we have is on our doorstep" as he called for a "new special relationship" with the EU.
The former minister, who has confirmed he would enter any potential leadership contest, added "Britain's future lies with Europe – and one day back in the European Union".
Burnham has formerly said he would like to see the country re-enter the EU "in my lifetime", but on Monday emphasised that he did not believe now was the time to reopen that debate.
He argued that Brexit had been "damaging" but said Britain would be "stuck in a permanent rut if we are just constantly arguing and pulling away from each other".
The Labour manifesto said the UK would "stay outside the EU" and seek to "make Brexit work", with a push for closer ties but "no return to the single market, the customs union, or freedom of movement".
Burnham is hoping to return to Parliament by seeking the nomination to be his party's candidate in the Makerfield, a constituency where 65% of people backed Brexit.
The BBC understands the by-election will likely take place on 18 June.
Asked if he would set a timetable for his departure in the event Burnham became the MP for Makerfield, Sir Keir said "I'm not going to do that" adding that the by-election is "a fight between Labour and Reform, it's a very important fight, I will be backing 100% whoever the [Labour] candidate is".
He said Labour members needed to put aside "whatever views people have about the future of the party" and back Labour's candidate in the by-election.
Pressed on his own political future, Sir Keir said he wanted to fight the next general election but that he recognised that "we've got to turn things" after the party's dire election results on 7 May.
Speaking earlier in the day, Deputy Prime Minister David Lammy said there had been an "extraordinary own goal for 10 days" and said Labour MPs needed to remember that they are in government.
He told BBC Radio 4's Today programme: "I say to colleagues, 10 days of this, fine, I think the British people will forgive us for the introspection.
"Ten weeks of this and we're in desperate trouble, we'll be out of office and what we'll be ushering in is Farage."
The contest in Makerfield was triggered by the resignation of Labour MP Josh Simons, who said he believed Burnham could "drive the change our country is crying out for".
The seat was won by Labour in 2024 with a majority of 5,399 votes over Reform.
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 won roughly 50% of the vote share in the area.
Farage has said Reform "will throw absolutely everything at" the by-election contest.
Labour MP Jonathan Hinder said the party "took a real beating in our working-class heartlands" in the local elections to Reform, which was previously known as the Brexit Party.
He told the BBC: "The idea that we can reconnect to our working-class base by reopening this debate is just a staggering level of out of touch."
Liberal Democrat Europe spokesperson Al Pinkerton MP said Burnham had u-turned on his view of the EU, adding: "The Liberal Democrats have always been clear that Britain's future lies back in the EU and we have a credible plan to get there, starting with a customs union."
Conservative Party Chairman Kevin Hollinrake responded to Streeting's comments by saying "whilst Labour relitigate Brexit, Britain is not being governed".
On Monday, Lammy said he began the process of the UK "getting closer to Europe" during his time as foreign secretary and the government "set our red lines in the manifesto, we stand by those red lines".
He also likened Brexit speculation to a "sixth form debate".
