Gordon Brown today sought to face down his critics, vowing that he would not "walk away" in the face of political and economic difficulties.
Addressing Labour activists in East London he pledged to push on with measures to tackle the recession and clean up Parliament.
"What would they (the public) think of us if ever we walked away from them at a time of need. We are sticking with them," he said.
Mr Brown acknowledged that the country was going through a difficult time but he insisted that it was Labour values that were needed to deal with the crises in the economy and MPs expenses.
"This has been a testing time for our whole country, not just for the economy of our country but the whole politics of our country," he said.
"What has been happening over these last few months is a test not just of our character, a test not just of the Government, it is a test of our beliefs.
"If we believe that people should be responsible and people should act fairly and we should be fair to others, then it is our duty to make sure in our politics, in our economy, in our society, that's what happens."
His speech came just hours before the results were announced in the European elections which were expected to deliver another mauling for Labour.
There was speculation that Labour could be beaten into third or even fourth place behind the UK Independence Party - triggering a threatened revolt by rebel backbenchers.
Earlier, former Lord Chancellor, Lord Falconer, became the most senior figure yet to break cover and call for a leadership contest.
"I think we are moving moderately quickly towards the need for a change and that change may be a change in leadership," he told the BBC1 Politics Show.
"We need unity above all. Can we get unity under the current leadership? I am not sure that we can and we need to debate it urgently and I think probably it will need a change in leader."
Meanwhile, Cabinet Office Minister Tessa Jowell became the first member of the Cabinet to suggest openly that Mr Brown could be prepared to stand down as Prime Minister if he believed he had become an "obstacle" to Labour's recovery.
Asked on BBC Radio 4's the World This Weekend if Mr Brown would be prepared to step aside if his senior colleagues told him that it was time to go, she said: "Gordon Brown loves the Labour Party, he is Labour through and through.
"If Gordon Brown were to reach a conclusion that he personally was an obstacle to Labour's recovery and achievement, then of course like Tony Blair did...
"In the very bad days when Tony Blair was Prime Minister, that is precisely what Tony Blair said."
Aides insisted that she was not suggesting Mr Brown should stand down. She was said to have been thinking of events in 2004 when she and other ministers persuaded Mr Blair to carry on at a time when he was considering quitting.
Nevertheless, by accepting the proposition that Mr Brown could be persuaded to go, she only intensified the increasingly febrile mood at Westminster.
Lord Falconer's call for a leadership contest was swiftly rejected by newly promoted Home Secretary Alan Johnson, who is widely regarded as the most likely successor if Mr Brown is ousted.
"I don't agree that regicide gives you a unified party," he told the Politics Show. "I think that Gordon Brown is the best man for the job."
Lord Falconer - Mr Blair's old flatmate - denied that he was part of a "Blairite plot" against Mr Brown but warned that the Prime Minister may find that his hand was forced if he was not prepared to go of his own accord.
"The Prime Minister first of all has got to consider what he thinks the mood of the party is. If he concludes that he should go then there will be a leadership election," he said.
"If on the other hand he concludes that's not the position, then, in the light of what's been happening, somebody - and I think there'll be more than one - can decide whether or not they would wish to seek the 70 signatures that would be required to challenge a leader."
Earlier, Business Secretary Lord Mandelson cast doubt on the ability of the plotters to put up a credible candidate against Mr Brown.
"It would require somebody to stand against him, somebody who is raising their standard and saying that they could do a better job and we don't have that person," he told BBC1's The Andrew Marr Show.
He told the rebels to "stop taking shots" at the Prime Minister and warned that they faced the prospect of having to fight an immediate general election if Mr Brown went.
"If we were to have a third leader in a single parliament it would mean irresistible pressure to hold a general election," he said.
However Nick Raynsford, another former minister who has been calling on Mr Brown to stand down, said that tomorrow's meeting of the Parliamentary Labour Party would be an "important moment".
While he insisted that he was not part of an "organised conspiracy", he warned that Labour would be heading for electoral disaster if they carried on as they were.
"We have seen over the last week a whole series of events all indicating the profound unhappiness of very many MPs, and indeed many party members," he said.
"I am afraid that if we don't take the right decision now that mood of unhappiness will continue. We will have a long lingering downward decline towards what I see at the moment as almost inevitable electoral defeat next year.
"That would be disastrous."
It was unclear how much support the rebels can command, with key figures on the left of the party dismissing the plot as a "Blairite coup".
Backbencher Diane Abbott told Sky News: "All the key figures are Blair acolytes. It is a Blairite coup that went off at half-cock."
Jon Cruddas - who finished third in the 2007 deputy leadership contest - warned that it would be mistake to get rid of Mr Brown with a general election less than a year away.
"Everyone knows our Government is in trouble. Serious trouble. But to suggest that we'll tackle those problems simply by chucking Gordon Brown overboard is madness," he said.
Senior party figures fear the results of the European elections due out this evening could be even worse than the local council elections which saw it lose more than 270 seats and the control of its last four English counties.
There is speculation that Labour could be beaten into a humiliating third or even fourth place behind the UK Independence Party (Ukip) and the Liberal Democrats.
Such a devastating result could act as a catalyst for rebel MPs plotting to oust Mr Brown in a so-called "peasants revolt" finally to show their hand.
Voting in the European elections took place on Thursday - the same day as the English council elections - but the results are not being announced until after the polls close right across the EU tonight.
A combination of disillusion with the major parties in the wake of the MPs expenses scandal and a system of proportional representation that helps the smaller parties mean it could be a particularly difficult night for Labour.
Smaller parties like Ukip - who beat the Lib Dems into fourth place five years ago - the Greens, and the far-right British National Party will be hoping to make gains, particularly if the turn out is low as supporters of the main parties stay away.