Tackling gangs should be the "new national priority," the Prime Minister said as he blamed the recent riots on selfishness and family breakdown.
The Prime Minister said a "social fightback" must follow the security response already announced.
He began by attacking "moral neutrality" and relativism, where bad choices were explained as merely "different lifestyles".
"We have been too unwilling for too long to talk about what is right and what is wrong," he said from Oxfordshire.
"We have too often avoided saying what needs to be said - about everything from marriage to welfare to common courtesy."
He blamed irresponsibility, selfishness and absent fathers for the riots as he and the Labour leader both delivered speeches offering their analysis of the nation's social problems.
Describing the spate of disorder as a "wake-up call for our country", Mr Cameron said there had been a "slow-motion moral collapse" in the UK.
"Irresponsibility. Selfishness. Behaving as if your choices have no consequences. Children without fathers. Schools without discipline," he said.
"Reward without effort. Crime without punishment. Rights without responsibilities. Communities without control.
"Some of the worst aspects of human nature tolerated, indulged - sometimes even incentivised - by a state and its agencies that in parts have become literally de-moralised."
He called for an "all-out war" on gangs and gang culture, with tough punishments matched by a wider social agenda.
The Prime Minister said he believed many rioters came from families with no father at home and communities where that seems normal.
Policies will now have to pass a "family test" to ensure they support the values that keep people together, he explained.
Mr Cameron also said the recently-introduced National Citizen Service should be available to all 16-year-olds as a rite of passage.
He said the non-military programme "captures the spirit of national service" and can teach team-work to alienated youths.
But as soon as he finished his speech, Labour leader Ed Miliband delivered his own analysis of the social problems facing the country.
He restated his call for a full-scale inquiry into the riots and warned against knee-jerk policy responses.
Mr Miliband agreed parental and individual responsibility are factors but said looters have not been the only ones to demonstrate greed and selfishness.
"It's not the first time we've seen this kind of me-first, take what you can attitude," he said.
He said reckless bankers, greedy MPs and phone-hacking journalists all helped create this culture.
In an indirect attack on the Prime Minister, Mr Miliband said merely blaming others for the riots - the police, parents and a so-called underclass - was too simplistic.
He also challenged Mr Cameron's view of family breakdown, arguing some single parents do a brilliant job while some two-parent families fail.
Speaking from his old comprehensive school in north London, he continued: "The small minority who did this are not one race, one community, one age group.
"They are British people from Brixton to Gloucester, Croydon to Manchester.
"And to answer what has happened, we have to state the most inconvenient truth of all: yes, people are responsible for their actions.
"But we all bear a share of responsibility for the society we create," Mr Miliband added.
Shadow minister Tessa Jowell backed his call for an inquiry that engages with communities and listens to the wisdom of people with experience of tackling issues such as gangs.
She told Sky News the the opposition want "real change" that takes place "under the radar of screaming headlines".
Now the immediate security concerns appear to have passed, both leaders want to seize the initiative politically.
But Work and Pensions Secretary Iain Duncan Smith said cross-party cooperation was key.
"We've got to stop nit-picking, playing games with this, pretending there's some kind of political advantage to be gained," he told Sky News.
"The truth is we are all in this one together and we've got to get out of it together."
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