The PM said he was responsible for the poor results, but Labour would recover
Labour ministers are rallying round Gordon Brown following a disastrous showing in the local elections.
The prime minister is under attack from some backbenchers after huge losses.
Some MPs are demanding more details about the compromise over the abolition of the 10p tax rate amid media reports of a series of policy adjustments.
Among those saying there is no threat to Mr Brown are foreign secretary David Miliband, deputy leader Harriet Harman and health minister Ben Bradshaw.
International Development Secretary Douglas Alexander has also come to the prime minister's defence, as has chairman of the Parliamentary Labour Party Tony Lloyd.
On Sunday, the prime minister promised to listen to, and learn from, the voters.
Joining Mr Brown's allies who are dismissing talk of a leadership challenge, Mr Lloyd told BBC Radio 4's Today programme the prime minister's position was not in question.
"There isn't, outside of those who have their own personal malice towards Gordon or indeed the odd ones with personality defects, a challenge against Gordon Brown.
"What there is, is a demand of Gordon Brown to... begin to do what Labour MPs have been saying to him, to make sure that the policies are consistent with Labour's overall position as a party of fairness and social justice," he said.
International Development Secretary, Douglas Alexander, said the government would continue to help people worried about the economy and their household budgets.
"We believe that you shouldn't leave people defenceless in the face of economic change, you should work alongside people to support them.
"That is partly why - notwithstanding the success of the Conservative Party last Thursday - I would defy anybody to tell me what is a coherent modern Conservative response to some of those challenges that we're facing."
Business secretary John Hutton called on Labour backbenchers to support the prime minister and health minister Ben Bradshaw said despite current problems he remained the right person to lead the party into the next election.
"When we get through this, people will look back and say he was the right man in the right place, and they'll have to make a choice between that and the alternative, which I don't think is a very attractive one," said Mr Bradshaw.
Mr Hutton said suggestions from some Labour backbenchers that Mr Brown had just six months to save his job were ludicrous.
"All that talk about a leadership challenge is nonsense, a complete irrelevance," he said.
Deputy leader Harriet Harman urged MPs to stop "navel gazing" about Labour's internal disputes.
Some Labour MPs are calling for a shift in policy back to traditional Labour concerns like rail re-nationalisation, council-house building and taxing the rich.
Gower MP Martin Caton said the party should "start talking about really tackling poverty, and that... is going to have to mean that the richest people in society contribute more".
Former minister Peter Kilfoyle said the government needed to refocus its efforts on those people who had deserted the party because they felt the government had "left them out."
Influential backbencher Jon Cruddas also warned: "Our people are abandoning us, we're sinking fast, and no amount of hand-wringing and promises of 'listening and learning' from election night will change that."
He said it was not too late for the party to "choose change".
There is speculation in the newspapers that the party's future plans might include a raft of policy changes, including scrapping plans to charge households according to how much rubbish they throw out.
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The Tories might get in by default, on the back of Browns' mass of failures rather than actual merit
On Sunday, Mr Brown said Labour "will recover" after its worst local election results in 40 years, and told the BBC he took the blame.
Labour's poor local election results - in which their projected share of the national vote dropped to 24%, pushing them into third place behind the Lib Dems - were topped by Ken Livingstone's defeat by Conservative Boris Johnson in London's mayoral race.
In his first interview after the results were announced, Mr Brown said it had "not been the best weekend", adding that voters were worried about rising petrol and food prices and utility bills.
Meanwhile former minister Frank Field, the leader of Labour's backbench revolt against scrapping the 10p tax rate, threatened to revive the protest.
He urged Mr Brown to specify how those affected will be compensated and said unless Mr Brown made the package "crystal clear" several MPs were prepared to block the Budget.