Andy Burnham and Wes Streeting, who are both former health secretaries, are widely thought of as rivals for a potential Labour leadership election.
The first weekend of campaigning is set to get under way in Makerfield, in a by-election that Andy Burnham said could “change Labour”.
Mr Burnham, who is viewed as a challenger to Sir Keir Starmer in a potential Labour leadership race, launched his by-election campaign on Friday and promised he was not offering “more of the same”.
Allies of Mr Burnham have suggested he may not launch a bid for the party leadership immediately if he is successful in his attempt to return to Parliament in the June 18 contest.
But Wes Streeting, who resigned from the Cabinet earlier this month, has openly talked about launching a campaign to oust Prime Minister Sir Keir.
The MP and former health secretary told reporters on Friday that he held off triggering a leadership race to give Mr Burnham time to tread a path back into the Commons.
In a pitch to voters, Greater Manchester Mayor Mr Burnham said: “I know my own party needs to change. We need to be better than we have been.
“A vote for me in this by-election is a vote to change Labour.”
Mr Burnham, who is also a former health secretary, later told reporters Labour has “space to be more radical” while honouring the party’s 2024 general election manifesto.

This could include council tax reforms, targeting the construction of more council houses, considering the abolition of inheritance tax and bringing in a care levy.
He also said he thought the Government was “moving in the right direction” on immigration but suggested ministers should consult on the proposals.
His campaign appears to have the backing of several Labour figures who have criticised Sir Keir.
Mainstream, a Labour pressure group, has announced plans for former first minister of Wales Mark Drakeford to join the campaign trail in early June.
Mr Drakeford told Channel 4 News earlier this week that Sir Keir’s premiership “hasn’t worked out – it’s time to recognise that and make a plan to move ahead”.
Also listed are Simon Opher, the Stroud MP who has called for an “orderly transition that brings together the very best talents across the Labour Party”, and Liverpool Wavertree MP Paula Barker, who previously told the BBC: “Andy would be the person that I would like to see lead our party.”

Mr Burnham faces Reform UK’s Robert Kenyon in the by-election, a plumber who said he is “ready to take on the King of the North” in a reference to Mr Burnham’s moniker.
Mr Kenyon was joined on the campaign trail earlier this week by his party leader, Nigel Farage.
The Liberal Democrats unveiled Stockport councillor Jake Austin as their candidate to contest the seat, who said voters in Makerfield “deserve so much more than the failing Labour Government or the divisive politics of Reform UK”.
The Conservatives have named Michael Winstanley as their candidate, while the Greens on Thursday named Chris Kennedy, who withdrew from the race shortly after his selection.
The party said Mr Kennedy had withdrawn for “personal and family reasons”, but it later emerged that he had shared posts on social media claiming an attack on Jewish ambulances in north London had been a “false flag” operation.
A Green spokesperson said Mr Kennedy had deleted and apologised for the posts, but added the party stood by its previous statement about the reasons for his withdrawal.

In an interview with the Mirror newspaper, Mr Streeting backed Mr Burnham’s campaign.
“We need all of our best players on the pitch,” he said.
“We’ve obviously got the Makerfield by-election underway, where Andy Burnham has my full support, and I suspect Andy Burnham would want to be a candidate in a leadership race.
“And I felt that if I’d rushed ahead and triggered a leadership contest before Andy Burnham had the chance to come back, people would have just said I was trying to pull a fast one, trying to get ahead of the competition.”
Mr Streeting also unveiled one of his “first campaign pledges” – to “fund the full restoration of Sure Start”.

The Ilford North MP said: “It would show that this Labour Government, and a Labour government I lead, is absolutely committed to building a better future for the next generation, making sure that kids – all kids – get the very best start in life, closing that gap that sees kids from poorer families arrive at school with their futures already determined, already disadvantaged from those from the more wealthier backgrounds.”
He added he would pay for the proposal with a wealth tax, building in carve-outs for “things like entrepreneurs’ allowances and investment allowances to encourage those wealth creators to invest in the sort of businesses that will improve our growth”.
Speaking to the Guardian, he suggested making the independent Planning Inspectorate more involved in approving new housing and easing some of the thresholds at which housing developers must carry out an environmental assessment of their proposals.
He also insisted he had the numbers to launch a leadership bid, “including ministers”, before he held off triggering one.
Josh Simons, the Labour MP who stood down to make way for Mr Burnham, won in 2024 by just 5,399 votes, while Reform comfortably won every ward in the constituency at this month’s local elections.

