Ex-health secretary Andy Burnham says he wants to stand for Labour leader and "rebuild the party for new times".
He told the Daily Mirror newspaper the party owed a "debt of thanks" to Gordon Brown and Tony Blair but said he would end "stage-managed" politics.
He said Labour had to understand voters’ sense of "unfairness" and that Labour lost because they felt "our priorities were not their priorities".
David and Ed Miliband, John McDonnell and Ed Balls also intend to stand.
They must get the backing of 33 Labour MPs each by Thursday 27 May, if they are to get on the ballot paper.
In an article for the Mirror, Mr Burnham – who held three cabinet posts under Gordon Brown’s premiership – said the party "must avoid looking like we are disowning the past".
‘Sense of unfairness’
But he said Labour had to be "honest" about why it had lost power.
"I heard the same echo everywhere I went. People trying to get on in life and do the right thing felt Labour was no longer at their side.
"Our priorities were not their priorities: that we were doing more for those who didn’t want to work than those in work but struggling, particularly with no children; that we were in denial about the effects of immigration – on wages, housing and anti-social behaviour – in places where life is hardest; and that pensioners who had done the right thing and saved found they were above the line for help.
"Labour won’t be heard again until we show that we understand this sense of unfairness."
He said they had sometimes given the impression Labour had "no views about pay at the top of the scale" and would have picked up on the issues if it had been connected to "our own grassroots".
He said Labour had been "too controlling and cautious" and must become a "people’s party", reducing the influence of "small elites at the top".
He also said the party "should bring down the final curtain on the era of stage-management in politics, making our party conference a forum for real debate and drama once again".
‘Team player’
Mr Burnham pledged to make it cheaper to join the Labour Party and said he could make it "welcoming and unifying", adding: "I am a team-player, I’ve never had time for factions."
Mr Burnham, 40, has been MP for Leigh, Greater Manchester, since 2001.
He held the posts of chief secretary to the Treasury, Culture Secretary and Health Secretary under Gordon Brown’s premiership.
He has also worked as a special adviser in the Department for Culture, Media and Sport, a research assistant to Tessa Jowell and parliamentary private secretary to David Blunkett, when he was home secretary.
He is the fifth Labour MP to enter the race. The winner will not be announced until 25 September.
On Wednesday Ed Balls launched his campaign, saying he wanted to "listen first, hear what the public say". Mr Balls, a close ally of Mr Brown, added the contest was not about "Blair versus Brown" or "old Labour versus new Labour".
"I think that’s the past really – what people want to know is, are we in touch with the public, are we on their side, do we understand their concerns?"
MPs who want to get on the ballot paper have until Thursday 27 May to gather the backing of 33 MPs – a timetable some have said is too tight, particularly for less high-profile candidates.
Left-wing MP John McDonnell said he wants to stand but the timetable makes it "almost impossible" and argues that the process has been "stitched up from the start".
Ed Miliband has also said it should be longer. On his Twitter page, he wrote: "MPs/members annoyed about short nominations timetable: I have to say I agree. Need broadest possible choice & time for MPs to decide&consult".
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