I won't walk away, insists Brown
Gordon Brown has unveiled a reshuffled cabinet and vowed to "fight on" with his "resilient" team to rescue the economy and clean up politics, BBC reported.
He admitted Labour had suffered "a painful defeat" in Thursday's polls but added: "I will not waver. I will not walk away. I will get on with the job."
And he unveiled Glenys Kinnock as Europe minister in a surprise move.
Two more cabinet ministers - Geoff Hoon and John Hutton - have stepped down but neither backed a challenge to the PM.
Speaking at a Downing Street media conference, Mr Brown said the current political crisis, fuelled by the Westminster expenses scandal "is a test of everyone's nerve - mine, the Government's the country's".
He added: "If I didn't think I was the right person to lead these challenges I would not be standing here.
"I have faith in doing my duty... I believe in never walking away in difficult times."
Labour MP Ian Gibson says he is standing down to force a by-election in Norwich North - saying he thinks Mr Brown's days "are close to being numbered".
In other moves, Alan Johnson becomes home secretary and Andy Burnham succeeds him at health.
Mr Hoon has agreed to be the prime minister's European policy adviser ahead of the Climate Change talks in Copenhagen at the end of the year.
Bob Ainsworth becomes defence secretary and Peter Hain returns to the cabinet in his old job of Welsh Secretary. Ben Bradshaw enters the cabinet as culture secretary and Lord Adonis takes over transport.
Universities Secretary John Denham succeeds Hazel Blears as communities secretary and Yvette Cooper replaces Mr Purnell as work and pensions secretary, with Liam Byrne replacing her as Chief Secretary to the Treasury.
Margaret Beckett and Paul Murphy are amongst those resigning from the cabinet.
John Hutton earlier quit as defence secretary and James Purnell quit on Thursday as work and pensions secretary - but no ministers have so far backed Mr Purnell's call for Mr Brown to "stand aside".
Mr Hutton backed the prime minister said he thought fellow Blairite Mr Purnell had made "the wrong decision" in calling for him to quit.
"I'm not going to be contesting my seat in the next general election and I think it's absolutely right that Gordon, who I'm supporting as our prime minister and party leader, should have a cabinet that's going to take him through the next election and beyond," Mr Hutton told the BBC.
Alan Johnson, touted by some backbenchers as a possible leadership challenger, said he backed Mr Brown "to the hilt" to continue as prime minister.
He said he would "never say never" to becoming prime minister at some point, but insisted he could see no circumstances at present where he would mount a bid for the job.
He insisted that Mr Brown was "absolutely the best person for this job" and took a swipe at Mr Purnell, saying: "It is a difficult job at the best of times and it is not a job that his own colleagues should be making more difficult through their own actions."
BBC Political Editor Nick Robinson said Mr Hutton's decision not to attack Mr Brown - coupled with Mr Johnson's loyalty - had shored up his position as prime minister.
But Gordon Brown was not getting the reshuffle he had planned a week ago, he added.
Alistair Darling had turned down a move to the Home Office and Mr Purnell had been "sounded out" about the job of education secretary, which would have paved the way for Mr Brown's ally Ed Balls to become chancellor, but that was not now going to happen.
According to the BBC's projected share of the national vote at a general election, based on the English local election results in so far, the Conservatives would poll 38%, the Lib Dems 28% and Labour would be third on 23%.
Although no cabinet ministers have backed Mr Purnell, some Labour MPs and senior figures in the party, including former chairman of the Parliamentary Party Lord Soley and senior backbencher Barry Sheerman, have said there has to be a change of leadership.
And Dr Gibson - stripped of the right to stand for Labour at the next election because of his expenses claims - said he would stand down now to trigger what is likely to be a potentially difficult by-election for Labour.
Conservative leader David Cameron and Lib Dem leader Nick Clegg repeated their calls for a general election.
Mr Cameron told BBC News the government had "lost the right to govern," adding: "We have a government in complete chaos. We really do deserve better than this."
Mr Clegg said Mr Brown's future as PM was "irrelevant" because the Labour government was "finished" and had "run out of road".
The results of the European election, which was also held on Thursday, will start to be published from 2100 BST on Sunday.