Wes Streeting has said he would "be prepared" to trigger a Labour leadership contest to replace Sir Keir Starmer as prime minister as early as next week.
The former health secretary told BBC Newsnight that "uncertainty and paralysis" in the Labour leadership would have to be resolved if the party wins Thursday's Makerfield by-election.
Both Streeting and Greater Manchester Mayor Andy Burnham have said they would stand in any contest to replace the prime minister, but previously shied away from saying whether they would trigger such a contest.
Speaking to reporters at the G7 summit in France, Sir Keir reiterated his intention "not to walk away" but to "carry on with what I was elected to do".
Burnham is standing to return to Parliament in the upcoming Makerfield by-election. If he wins and becomes an MP, he will be able to initiate or join a leadership race - something he is currently unable to do.
Asked by BBC Newsnight's Victoria Derbyshire if he would trigger a contest if Burnham wins, Streeting said: "I think the prime minister should be given some space and time to reflect over the weekend and I think we should see where we are then.
"I would prefer the PM to take a decision on his own terms rather than leave it for me or Andy or anyone else to trigger a contest.
"If not we can't carry on with this uncertainty and paralysis and there will need to be a contest and I would be prepared to do that."
Streeting earlier told the BBC he had the backing of the 81 Labour MPs he would need in order to launch a leadership challenge.
At an event earlier on Tuesday, the former health secretary said any Labour leadership contest must not become a race of who can offer "the most expensive and popular pledges to the party faithful at the expense of the British people".
He told an audience in central London he would not use a leadership campaign to make costly promises that he would have to later reverse.
Streeting resigned from government last month, accusing the prime minister of "drift" and a lack of vision.
In an hour-long speech, he set out his own vision for the economy, seeking to present himself as the financially responsible candidate who would encourage growth and bring taxes down.
Polls have suggested that Burnham is more popular with Labour Party members and Streeting himself said he would be the "underdog" in a contest.
But the former health secretary seemed keen to sketch out the battleground and strike the first blows, in a "battle of ideas" over the party's future direction.
In an apparent dig at his leadership rival, Streeting cautioned against treating the bond markets, where the government borrows money, as "Bond villains," adding: "We must reject the reckless approach that says 'stuff the bond markets'".
Last year, Burnham told the New Statesman magazine: "We've got to get beyond this thing of being in hock to the bond markets."
Earlier this year, in a bid to reassure international investors, Burnham promised to stick to the government's existing rules on borrowing.
In his speech, Streeting also contested Burnham's argument that the north of England had suffered from 40 years of "neoliberalism".
"It's more complicated than that," he said, adding: "We've been through several waves of change that have delivered genuine strengths, but also deep weaknesses."
Such was his emphasis on fiscal discipline - he cited former chancellors Gordon Brown and Nigel Lawson – some in the room mused whether he was making a subtle subsidiary pitch to be chancellor if he was the runner-up in a leadership race.
But he insisted he could win the top job by convincing Labour members that he could win a general election, and unite the centre with the left.
If he did become prime minister, he said he would rule out an early election and govern for the remainder of the parliamentary term.
Elsewhere, the Ilford North MP said that he wanted to see tax on employment come down when "the public finances allow" and repeated his call for capital gains tax to be equalised with income tax rates.
Asked if he would consider getting rid of the triple lock on pensions in order to pay for defence, Streeting said the measure, which guarantees certain rises in the state pension, was "here to stay for the entirety of this Parliament".
In a jibe at another Labour colleague, Streeting suggested Energy Secretary Ed Miliband should approve North Sea oil and gas drilling projects in Rosebank and Jackdaw.
"There is a pragmatic case for producing our own gas rather than importing from abroad," he said.
When in opposition, Miliband had described a licence issued to Rosebank as "climate vandalism".
A full list of the candidates standing in the Makerfield by-election can be found here.
