Education Secretary Alan Johnson has demanded an end to Labour squabbling to avoid the risk of "self-destruction".
In a speech which outlined his "Real Labour" vision he said only a unified party would secure a fourth term.
Mr Johnson, who has already said he wants to stand to be deputy leader, dodged questions about whether he was planning to now stand for party leader.
Elsewhere, as leadership speculation continues, Cabinet colleague Harriet Harman said she may stand for deputy.
And Ed Balls, Gordon Brown's closest ally, ruled himself out of the deputy leadership role, but said he could see Mr Johnson as leader.
'Self-indulgence'
In his address to the Social Market Foundation, Mr Johnson urged Labour not to "turn the clock back" or "close down new ideas".
After a week in which eight MPs quit government jobs over Tony Blair's refusal to give an exact timetable for his departure, Mr Johnson said: "Last week was not our finest hour.
"We must ensure that the self-indulgence of what was literally macho politics does not escalate into self-destruction.
"I suspect that Tony Blair gave him at least a very considerable hint or nod that he'd be gone in a shorter timescale than he is"
"There must be no resort to personal attacks either now or at any stage of the transition process.
"Britain faces enormous challenges which we must debate: responding to globalisation; healing ongoing social and religious divisions - as well as dealing with entrenched poverty, spreading opportunities to all."
Mr Johnson argued that these were not the ideological debates of the 1980s or early 1990s, such as Tony Blair's ditching of Labour's Clause IV commitment to nationalisation.
'Comradely debate'
He said the party must unify and connect with the public as it has over the last decade.
"There's no need to turn the clock back, cover old ground or seek refuge in entrenched positions," he said.
"Similarly, we mustn't stymie debate or close down new ideas. We've never made it to a third term before let alone renew in government.
"Now we need an honest, measured and comradely policy debate which will help us to a fourth term in government."
What was needed was the "distilling of old Labour and new Labour into real Labour", he said.
On Tuesday, Mr Brown told union chiefs he had no intention of reversing the prime minister's NHS reforms.
Johnson for PM?
Mr Balls, economic secretary to the Treasury, sidestepped questions on BBC Radio 4's Today programme over whether Mr Brown's ambition to be prime minister had been damaged by his perceived close involvement in the recent rebellion against Mr Blair.
Instead Mr Balls said there was a real desire for "unity" within the party.
Asked if he could see Mr Johnson running the country, he said: "Of course I could.
"The situation is moving on. Obviously I have to think about that, I have to reflect on that"
"There's going to be a transition over the next year, and the likelihood is that there is going to be a leadership election and there will be different candidates to come forward."
He said the next Labour leader will need to be trusted by the country and inspirational to the party.
On Tuesday, Northern Ireland Secretary Peter Hain announced his intention to stand as Labour's deputy leader when John Prescott stands down.
Asked whether she would stand, Ms Harman said the declaration by Mr Hain meant "the situation is moving on".
"Obviously I have to think about that, I have to reflect on that," she told BBC Radio 4's The World at One.
'Petty jealousies'
Meanwhile, ex-Tory deputy prime minister Lord Heseltine said he was sympathetic to Mr Brown's plight in having to wait a long time to become Labour leader.
"I suspect that Tony Blair gave him at least a very considerable hint or nod that he'd be gone in a shorter timescale than he is," he told BBC News 24.
But he said he felt ex-home secretary Charles Clarke's recent attack on the chancellor as "deluded" had "opened a can of worms about the personality of Gordon Brown".
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