Mr Burnham held three cabinet posts since 2007
Former Health Secretary Andy Burnham has said he wants to stand for Labour leader and "rebuild the party".
He told the BBC it was important for the candidates to discuss "differences of views" in an open debate.
Mr Burnham also said he disagreed with ex-Business Secretary Lord Mandelson's famous comment that he was "intensely relaxed" about people getting rich.
David and Ed Miliband, John McDonnell, Ed Balls and Diane Abbott also intend to stand for labour leader.
They must get the backing of 33 Labour MPs each by Wednesday 9 June, if they are to get on the ballot paper.
Mr Burnham, who held three cabinet posts under Gordon Brown's premiership, said many voters had felt "Labour was no longer on their side".
He added that he wanted to help people "fulfil their potential and break down the barriers that hold them back", as "Britain is a country where opportunities are still uneven".
'Differences of views'
Mr Burnham criticised the previous Labour regime, saying: "At the top of the pay scale, I think sometimes in the past we looked like we really didn't have an opinion... and society really changed when the credit crunch hit.
"People said this wasn't right and we need an assessment about what is fair pay."
He added: "Peter Mandelson said he was intensely relaxed about people earning large amounts, but I must say I'm not and that's a difference between Peter and me, and I'm happy to say that.
"As we go through a period of debate in the Labour Party, we have to discuss these differences of views."
Mr Burnham pledged to make it cheaper to join Labour and said he could make the party "welcoming and unifying".
The 40-year-old 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 Mr Brown's premiership.
The winner of the leadership race 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?"