Labour should not attempt to move away from the legacy of Tony Blair, the party's leadership frontrunner Andy Burnham has said.
In the first of a series of televised showdowns with the three other candidates vying to take the party's top job, the shadow health secretary said the former prime minister "did a lot of things right" and had reached out to voters who wanted to "get on in life".
Shadow health minister Liz Kendall, who is the candidate most closely identified with the Blairite strand of the party, insisted she was "not Blairite, Brownite, Old Labour, New Labour".
"I want to be today's and tomorrow's Labour," she added.
Ms Kendall appeared to suggest that Mr Burnham and rival Yvette Cooper had "baggage" as a result of their links to Blair and Gordon Brown.
"I think we do need a fresh start and I don't have the baggage of the past," she said.
Veteran left-winger Jeremy Corbyn said his party had "lost our way" and become "cowed" by powerful vested interests as he set out his stall in the hustings staged by BBC2's Newsnight in Nuneaton - one of several target seats Labour failed to win in the general election.
Pressed on how the party should distance itself from the Blair era and move more to the left, Mr Burnham said: "I don't think we would want to do that because Tony was the prime minister that won three elections Labour.
"But, he didn't get everything right so we have to learn from the mistakes of that government.
"But, he did a lot of things right and he spoke to people's wishes to get on in life.
"We have to as a party want to be the party that helps everyone get on in life and that's where Labour has got to be going forward."
Mr Corbyn won applause from the audience as he said that he had never been a supporter of New Labour
"Why oh why oh why did Blair have to get so close to Bush that we ended up in an illegal war in Iraq?" he said.
"The party has a opportunity now to rediscover its principled roots, rediscover the issues of equality, rediscover the issues of public service."
Ms Kendall said it was essential that Labour showed it was committed to tackling the deficit if it wanted to regain power.
"Too many people didn't trust us on the economy or with their taxes," she said.
"That is the basic test of competence for any party that wants to govern. We have to address that or we won't win in 2020."
On the issue of immigration, Mr Burnham said that the party had to show that it understood voters' concerns.
"Labour needs to get out of the Westminster bubble and this is the prime example. We have not realised how quickly immigration has changed some communities in this country," he said.
Ms Cooper said that there had to be "sensible" controls to show voters that the system was fair.
"We have got to have a sensible debate about immigration - no arms race rhetoric that just cause all kinds of problems and division," she said.
Ms Kendall acknowledged that pubic anger on the issue but said that it was important to understand the benefits immigration had brought.
"I will not be a Labour leaders who tries to out-Ukip Ukip or pretend to people there is some kind of button we can push to rewind the country and go back to a world that isn't coming back," she said.
Mr Corbyn issued the strongest defence of the contribution which immigrants had made to the country.
"If there hadn't been immigration to this country, what kind of health service would we have, what kind of transport system would we have, what kind of education system would we have? We would be in a much more difficult place."
Ms Cooper said that she believed the time had come for the Labour Party to elect a woman leader.
"For the Labour Party which has campaigned for women's equality for over a century, it would be fantastic for us to smash that final glass ceiling and elect a Labour woman leader of the party and a Labour woman prime minister as well," she said.
But she refused to be drawn on whether she would support Ms Kendall if she did not win the contest herself.
"I am not backing anybody else," she said.
Ms Kendall, when asked if she would resign before the next election if it looked like Labour were not going to win, said: "Yes, because more than anything I want Labour to win so we can change the country.
"Now, I think I'm going to be the Labour leader that the Tories fear and that's right because we need to win and we are forgetting our winning ways as a party.
"It has been too long since we won those major elections. If people think I'm not doing a good enough job, I think I'll prove that wrong but ...
"There are some MPs who are talking about having a new process whereby if colleagues think you are not doing well enough you can go.
"I have to go through that as a local Labour MP. We should have that for the Labour leadership too because above all we cannot put our values into practice unless we win."
Mr Corbyn said: "I think there should be an opportunity to elect or not elect the Labour leader regularly, every one or two years so that we don't go into this idea the leader's vulnerable, you have got to get rid of the leader or don't get rid of the leader."
Asked if there should be the opportunity to get rid of the new leader if they were not up to the job, Mr Burnham replied: "Of course there should. Yes is the answer to your question."
He added: "I'm somebody with my feet on the ground and I wouldn't do anything to harm the interests of the Labour party."
Mr Burnham said the party already had a rule that allows the leader to be ousted.
"The party comes first, always," he added, prompting Ms Cooper to jibe back: "The country comes first."
The shadow home secretary refused to back such a move, insisting the party already had the rules it needed to axe failing leaders.
"The last people who should be deciding what are the rules for this leadership contest are the people who are standing in the leadership contest.
"We should follow the rules that the party sets out."
Asked if she would subject herself to a re-election process, she replied: "I think there are already ways in the Labour party, procedures ... it's up to the Labour party to decide, not us."
Ms Kendall said the "whole" benefit system was failing and need to change.
"The whole welfare system is failing. It's not making sure that people who can work get the incentives and help they need to work and it's not providing any kind of decency for those who are really, really struggling and are ill."
Ms Cooper called for "responsible" language in the way the welfare is spoken about and recalled being off work for a year when she was seriously ill 20 years ago.
"I was desperate to get back to work. I hated every minute of it. I had to claim benefits because otherwise I wouldn't have been able to pay the rent. As a result, I would never say that people who can work are work shy or benefit scroungers."
Ms Kendall said voters did not trust Labour on the economy and taxes.
"We should be aiming for a surplus when the times are good because we want to bring our debt down so we can spend money on the things we really care about."
Mr Burnham said Labour "did let the deficit get too high" but rejected suggestions that achieving a budget surplus was top priority.
He added: "No, is the answer. What matters is a growing economy, decent jobs, strong public services."
Mr Corbyn said: "The most important thing is to ensure our community has a health service, has an education service, people are decently housed and young people have abilities to go into work and develop themselves."