Ed Miliband has blamed the riots that swept English cities on a "me first" culture - and accepted Labour must share the blame for creating it.
The Labour leader said his party had failed to tackle inequality and not paid enough attention to morality.
And he linked the riots to a wider collapse in social responsibility exemplified by the banking crisis and MPs expenses scandal.
He said he would set up his own riots inquiry if David Cameron failed to act.
Mr Miliband told BBC Radio 4's Today programme the breakdown in social order that occurred this week showed many people had lost their sense of right and wrong and there was a "me first" culture.
"There is an issue which went to all our souls - this is an issue not just about the responsibility and irresponsibility we saw on the streets of Tottenham.
"It's about irresponsibility, wherever we find it in our society.
"We've seen in the past few years MPs' expenses, what happened in the banks, what happened with phone hacking."
And he admitted that Labour had not done enough to tackle deep-rooted moral problems during its 13 years in power.
"I deeply regret that inequality wasn't reduced under the last Labour government. But we did great things to tackle inequality in our society," he told BBC Radio 4's Today programme.
"We did better at rebuilding the fabric of our country than the ethic of our country."
He urged the prime minister set up a public inquiry in the next few days, adding: "We have got to avoid simplistic answers.
"There's a debate some people are starting: is it culture, is it poverty and lack of opportunity? It's probably both."
Mr Miliband said that if Mr Cameron does not agree to set up an inquiry "I'm going to do it myself".
Speaking to a group of young people in Brixton, south London, Mr Miliband said the inquiry should not just take evidence from the "usual suspects" but should also include people from communities affected by the rioting.
The Commons Home Affairs Committee will begin its inquiry on 6 September, with London Mayor Boris Johnson set to be its first witness.
Committee chairman, Labour MP Keith Vaz, said: "We will be looking at police tactics, we will be looking at the operation of gangs, we will be looking at mobile communications, and we will be revisiting some of the issues we have looked at in the past, such as the inquiry into the G20 protests.
"This will be a thoughtful and measured inquiry."