Addressing supporters at a rally, Mr Brown said the country had changed "for the better and for ever" under 13 years of Labour government.
Reeling off a list of Labour achievements since 1997, Mr Brown said; "When people say politics cannot change anything - it can, it has and it will in the future."
Describing Labour as the "greatest fighting force for fairness", he said: "When we fight, fight, fight, we win."
Mr Brown said he had "never known" a situation in which so many people had yet to make up their minds, saying the future of the country depended on people's choices.
Arguing a Conservative government would endanger public services and result in millions of people being "left behind", he urged people yet to make up their minds to "come home to Labour".
"If it is style over substance, they win. If it is recovery over risk, we win."
Meanwhile, Mr Cameron told Conservative supporters in East Renfrewshire that the election was "not yet decided" and that he would be campaigning "through the night" in an attempt to drive home his message.
'Read my lips'
"Millions of people up and down this country are still to make up their mind about which box to put their cross in," he said.
David Cameron: "Where has Gordon Brown's moral compass been for the last four weeks?"
He launched his most personal attack yet on Gordon Brown, accusing the prime minister of the most "negative campaign anyone has fought in the history of modern British politics" and "making up untruth after untruth".
Suggesting Mr Brown had mislaid his "moral compass", he added: "If this is the son of a preacher man, I do not know what we are hearing".
Mr Cameron said Labour claims that the Tories would cut benefits for pensioners, such as pension credits, free bus passes and the winter fuel allowance, were scaremongering.
Under a Conservative government, he said, these benefits were safe, adding: "You can read my lips. It is a promise from my heart."
Mr Cameron said he would be campaigning non-stop over the next 36 hours, making a series of visits to nightshift workers in the north of England and the Midlands throughout Tuesday evening and early Wednesday morning.
Among those he will speak to include bakers, fishermen and ambulance drivers.
"We are going at it all night and all day... all the way to polling day. That is the way we are going to win the election."
The BBC's Ben Brown said critics were dismissing this marathon effort as a gimmick but the Tory leader wanted to show that he had the energy and that he was not complacent about the result.
Mr Brown has also pledged to fight "every inch of the way" and will be campaigning until midnight on Tuesday.
Nick Clegg: "Glasgow does not belong to the Labour party"
Earlier the prime minister said he would take responsibility for "whatever happens" on 6 May and if he "couldn't make a difference anymore", he would go off and do something else.
Meanwhile, Lib Dem leader Nick Clegg has urged disaffected Labour supporters to back his party, saying they had been taken "for granted" and his party was the only progressive alternative.
"Support us in our campaign in these vital last crucial hours of the election campaign and deliver the fairness, the difference, the real change that I think Britain deserve," he urged.
The latest poll to be published suggests that Labour have made ground at the expense of the Liberal Democrats.
A YouGov daily tracker poll for The Sun, conducted on 3 and 4 May, puts the Conservatives unchanged on 35%, Labour up two points at 30% and the Lib Dems down four at 24%.
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