Gordon Brown has faced his first head-to-head challenge in his campaign to lead Labour in a debate with two potential opponents.
Mr Brown is favourite to be prime minister when Tony Blair steps down
The chancellor said he "welcomed the contest" offered by left-wingers Michael Meacher and John McDonnell.
But Mr Brown insisted Labour could not return to the policies which had failed in the past.
Mr Meacher said a leadership debate was vital while Mr McDonnell stressed his opposition to the war in Iraq.
During the debate, organised by the Fabian Society, Mr Brown promised "prudent" government.
"My aim has always been that every single individual in this country should have the chance to realise their potential," he said.
"That they should be able to bridge the gap between what they are and what they have it in themselves to be able to become."
He added: "Progress for this country is not going to be down to the policies that failed in the past."
Mr Brown also suggested a government under his leadership could include more women.
"I want more women in Parliament, more women in the government, more women in the Cabinet," he said.
Earlier, in a BBC interview, Mr Brown admitted the government had made mistakes, including the way it had handled the Millennium Dome.
He further acknowledged there were "always lessons to learn" from criticism he had indulged in spin in the Budget by announcing a headline 2p cut in the basic rate of tax, even though other changes meant many people would not be better off.
In Sunday's debate, Mr McDonnell insisted that he could be a strong challenger in the leadership contest.
He will meet his left-wing opponent on Monday to decide which of them should go forward to stand against Mr Brown.
The eventual candidate will need to get the backing of 45 Labour MPs to enter the contest.
Mr McDonnell said the public wanted "someone for example who voted against the war in Iraq. All the other parties voted for it, and I voted against.
"I'm opposed to the privatisation of our public services. So issue by issue not only do I have support on the policy issues within the Labour Party, I also have support in the general public."
He added: "This campaign is about giving people a voice again."
(l-r) Michael Meacher and John McDonnell debate with Mr Brown
Mr Meacher was keen to stress the importance of having a debate within the Labour Party.
"The Labour party, throughout the hundred years of its history, has elected its leader every single time, except in 1931, which was very exceptional circumstances," he said.
"And I think people want to have an opportunity of a debate and a choice and that it is key that people choose and do not have a leaders imposed on them."
He added there was a "tremendous desire" to have the party as "a vibrant effective force which the leadership takes account of".
The party's ruling national executive committee met on Sunday and agreed to the timetable for both the leadership - and deputy leadership - contests.
Nominations for the contests will open on Monday at 1430 BST and close on Thursday at 1230 BST. There will be 10 hustings events before the results are announced at a special one-day leadership conference in Manchester on Sunday 24 June.
Earlier on Sunday, Mr Brown announced plans for "eco towns" to be created as part of a general increase in house building.
The chancellor said he wanted the 100,000 homes in "carbon neutral" communities to be built on old industrial sites.
The Conservatives insisted the idea of "carbon neutral" towns were announced last year by a housing minister.
Shadow chancellor George Osborne said: "It's another example of same old Labour, same old spin."
Mr Brown also confirmed his plans to give Parliament more power over things such as decisions to go to war.
But he rejected suggestions that the Iraq war had been a mistake and said he planned to visit the country.