Labour is in "the fight of our lives" but the party can win the next election, Lord Mandelson has said
The business secretary said a Labour government had "never been needed more than now", saying his party should behave as "fighters, not quitters".
He pledged his "undivided loyalty" to Mr Brown and urged the public not to let the Conservatives "off the hook", saying their appeal was "shallow".
The Conservatives said the speech was devoid of new ideas or policies.
Lord Mandelson praised Gordon Brown, saying he had "gripped" the global financial crisis when other leaders had made mistakes.
In response, the prime minister told the Labour conference, the last before the next election, it should be "proud" of Lord Mandelson's contribution to the party.
'Offer of change'
Lord Mandelson said Conservative leader David Cameron had pursued a policy of "concealment not real change" in his efforts to modernise his party and was not equipped to deal with the major economic challenges facing the UK.
Recalling his surprise return to the Cabinet last year, Lord Mandelson said he had returned to frontline politics because Labour was in "his blood and bones" and because of his admiration for the prime minister.
Labour should be proud of its achievements since 1997 but this would not be enough to secure victory at the next election.
"You win elections on the future not the past. This will be a change election. Either we offer it or the British public will turn to others who say they do."
The new Labour project, which Lord Mandelson helped devise in the early 1990s, was "far from complete", he insisted.
He said Labour needed to "explain with confidence, clarity and conviction" the differences between it and the Conservatives, saying the election was "still up for grabs".
Under Gordon Brown's leadership, he said Labour would win the next election if "we show the British people that we have not lost the fighting spirit and appetite for change".
The Conservatives were "shallow" in their appeal and had no answers on key questions such as how to rebuild the economy, support industry and spread growth more evenly across the UK.
He said that he had been involved in five elections and claimed to have known deep down which way the result would go - including the surprise Conservative victory in 1992.
He said that the next election was not yet decided and, during a speech which sought to rouse party spirits, he also announced an extension of the car scrappage scheme.
The Conservatives said the speech showed the government was "empty" at a time of national crisis.
"It is sad that Peter Mandelson did not appear to have a new idea or policy to offer," said shadow business secretary Ken Clarke.
"The speech largely consisted of school-boyish attacks on the Conservative Party."
Earlier, Chancellor Alistair Darling promised new laws within weeks to put an end to City bonuses which cause excessive risk-taking and threaten financial stability.
He said he was hopeful the economy would start growing again later this year but warned that the recovery was fragile and could not be taken for granted.
The prime minister will make his leader's speech to the conference on Tuesday with the opinion polls suggesting Labour is lagging well behind the Conservatives and with some MPs still publicly questioning his ability to turn the situation around.
Backbench MP Graham Stringer, a persistent critic of the prime minister, said it would be "extremely difficult" for the party to win the election with Mr Brown as leader.
But Chief Whip Nick Brown told the BBC Mr Stringer was a "lonely and isolated" figure and Labour was united behind Gordon Brown.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.