Gordon Brown said he had the "new ideas and vision" to govern Britain as he launched his long-awaited campaign to lead Labour and become prime minister.
He praised Tony Blair and said he wanted to make the UK "one of the great success stories of the new century".
But the launch suffered a hitch with Mr Brown's face obscured on TV coverage of his speech by glass autocues.
Mr Blair earlier endorsed Mr Brown's bid to succeed him as prime minister, saying "he has what it takes".
Launching his campaign at the Imagination Gallery in central London, Mr Brown said Mr Blair "has led our country for ten years with distinction - with courage, passion and insight".
But he added: "In the weeks and months ahead, my task is to show I have the new ideas, the vision and the experience to earn the trust of the British people."
Mr Brown said he welcomed challenges from other leadership contenders and pledged to lead a government "of all the talents," refusing to rule out employing ministers from other parties.
Standing in front of his campaign logo, "Gordon Brown for Britain", Mr Brown pledged to tour the country to "listen and learn" about people's concerns.
"I want to lead a government humble enough to know its place - where I will always strive to be - and that is on people's side," he said.
He rejected Conservative calls for a snap election, saying the Tories did not call for an election in 1990, when Margaret Thatcher stood down.
He also denied he would move the government to the left, saying he would continue to "drive forward" New Labour reforms to the public services.
But he said he wanted to strengthen Britain's constitution and give more power to MPs.
"One of my first acts as prime minister would be to restore power to Parliament in order to build the trust of the British people in our democracy.
"Government must be more open and more accountable to Parliament - for example in decisions about peace and war, in public appointments and in a new ministerial code of conduct."
Mr Brown also suggested Britain could get its first written constitution, saying: "We need a constitution that is clear about the rights and responsibilities of being a citizen in Britain today."
On Iraq, Mr Brown said: "I accept that mistakes have been made."
He said he would be visiting Britain's troops and "listening to what the government of Iraq says".
Later, in a speech in Knebworth, in Hertfordshire, Mr Brown promised to create a "new kind of politics" in which the government "gives power away so that people in the community can have more power".
He said the challenge facing the government was to "create a strong society" to go with Britain's "strong economy".
Mr Brown is the firm favourite to succeed Mr Blair when he quits on 27 June.
He could still face a challenge from one of two left-wing backbenchers but there appears to be a coordinated effort among Labour MPs to unite behind him, with Blairite MPs Stephen Byers and Alan Milburn also expected to back him.
Mr Blair, who until now has held back from endorsing Mr Brown's bid to replace him, said: "I am absolutely delighted to give my full support to Gordon as the next leader of the Labour Party and as prime minister and to endorse him fully."
He added: "He has shown, as perhaps the most successful chancellor in our country's history, that he's got the strength and the experience and the judgment to make a great prime minister."
But shadow chancellor George Osborne, for the Conservatives, said Mr Brown as chancellor had been "responsible for the failures of the past 10 years".
"When you look at the things people are really fed up with, like the collapse of the pension system, like the failure to get money to the frontline of the health service, Gordon Brown is more responsible for that than any other politician including Tony Blair," Mr Osborne told BBC News 24.
Referring to Labour's heavy election losses last week, he added: "I don't see how he could be the change that the country wants and the country voted for."
Liberal Democrat Treasury spokesman Vincent Cable said Mr Brown had focused too much on improving his image and criticised his "presidential" style.
He added: "When he has tried to change his personality for PR purposes, it's been excruciatingly embarrassing... I think he's much better off being himself."
Mr Brown is spending the day touring marginal Labour seats which the Tories are targeting.
Commons leader Jack Straw, Mr Brown's campaign manager, said he wanted to "reach out" to the voters in the South-East of England that had brought Labour to power in 1997.
Mr Straw also denied suggestions there would be a cooling in relations between Downing Street and Washington under a Brown premiership.
He told BBC Radio 4's Today programme: "Gordon Brown and George Bush don't know each other anywhere nearly as well as Tony Blair and George Bush. That relationship will develop."
Backbenchers Michael Meacher and John McDonnell are still trying to muster enough support between them to mount a leadership bid.
They will meet on Monday - when nominations officially open - and the one with the fewest confirmed backers will stand aside.