David Cameron has said tackling the "broken society" is back at the top of his agenda following last week's riots.
He said he would review all policies, speed up plans to improve parenting and education and turn around the lives of 120,000 "troubled" families.
To tackle a "moral collapse" he pledged a war on gangs, but the home secretary said there would be "no quick fixes".
Labour leader Ed Miliband accused the PM of looking for "superficial answers" instead of lasting solutions.
As the two politicians gave speeches, courts continued to hear cases of the hundreds of people involved in rioting, looting and disorder across England.
In other developments:
- The Metropolitan Police have charged a 16-year-old boy with the murder of Richard Mannington Bowes, 68, who was attacked during rioting in Ealing, London, last week. The boy also faces charges of violent disorder and committing four separate burglaries of commercial premises
- Total arrests across seven police forces by Monday morning were 2,772.
- By noon, more than 1,179 people had appeared before the courts, the Ministry of Justice said, mostly on charges related to burglary, theft and handling, violence and violent disorder - 65% of people charged were remanded in custody.
- Two men and a 17-year-old boy have appeared in court charged with the murders of three men hit by a car in Birmingham last week. Another man was arrested on Monday - three others are already on bail
- Gordon Thompson, 33, has appeared in court charged with starting a fire which destroyed the 150-year-old House of Reeves furniture store in Croydon
- Work and Pensions Secretary Iain Duncan Smith tells the BBC that people convicted of involvement in rioting could lose their benefits even if they are not jailed
A Downing Street source has told the BBC there will be a "community engagement exercise" in communities affected by the disorder but said it would not be a formal inquiry.
Mr Miliband has been urging a community-based inquiry into the riots while a Lib Dem source said Deputy Prime Minister Nick Clegg had been brokering a deal for a "victim and communities commission" into the causes of the violence.
In a speech in Oxfordshire, Mr Cameron described the disorder that spread from London to parts of the East and West Midlands, Merseyside, Bristol, Manchester and Gloucester as "a wake-up call for our country".
He said politicians had been unwilling to talk about rights and wrongs, but "moral neutrality" would not "cut it any more" and said "the slow-motion moral collapse that has taken place in parts of our country these past few generations" must be confronted.
He included children without fathers, schools without discipline and communities without control in a list of what he believed has gone wrong in parts of the country and said people were "crying out" for the government to act.
"The broken society is back at the top of my agenda," Mr Cameron said.
Over the next few weeks, he said ministers would "review every aspect of our work to mend our broken society".
He pledged a "concerted, all out war on gangs and gang culture", which he said was a "major criminal disease that has infected streets and estates across our country".
"Stamping out these gangs should be a new national priority," he said - adding that a cross-government programme would look at "every aspect of this problem".
He has already announced plans to give police more powers to demand face masks are removed and to allow "gang injunctions" for over-18s, launched in England and Wales in January, to be used for children and adults.
Tackling gang culture was the subject of a meeting involving Home Secretary Theresa May, ministers and Acting Metropolitan Police Commissioner Tim Godwin on Monday.
Mrs May said there were "no quick fixes" and every angle, including schools, communities and jobs and benefits, must be considered.
Mr Cameron also said he wanted a "family test" applied to all domestic policies to ensure they did not undermine or "stop families from being together".
Plans to improve parenting would be accelerated, including work to target "troubled" families - the prime minister said his ambition was that the government would "turn around the lives of the 120,000 most troubled families in the country" by the next general election in 2015.
More police officers were needed on the streets he said, pledging to cut bureaucracy and arguing that those demanding he reverse plans to cut police funding were "missing the point".
He wanted to push "faster" on plans to strengthen school discipline and said ministers would look at the Human Rights Act and health and safety legislation - which he argued had been misrepresented by some in a way that had undermined personal responsibility.
And, following concerns from senior police officers about his plans to take advice from US "supercop" Bill Bratton, he said the US had been dealing with the problem of gangs for longer and it was right to listen and learn to "inspirational" police chiefs.
Downing Street said that officials and ministers were "looking at a whole range" of options before deciding whether benefits should be cut for rioters and looters given non-custodial sentences - something raised by cabinet minister Iain Duncan Smith earlier.
But in a speech at his old school in north London, Mr Miliband warned against "knee-jerk gimmicks".
"The politician's instinct - reach for new legislation, appoint a new adviser, wheel out your old prejudices - will not meet the public's demand for real answers and deep rooted, lasting solutions," he said.
"We've heard it all in the last few days, water cannon, supercops, a daily door knock for gangs and today, more gimmicks. A prime minister, who used to say the answer was to hug a hoodie, now says the answer is to reform our health and safety laws.
"Day by day the prime minister has revealed himself to be reaching for shallow and superficial answers, not the lasting solutions the country needs, based on the wisdom and insights of our communities."
He urged a "national conversation" about the causes of the riots - arguing that commissions had been set up after previous major disturbances to look into the causes.
The police and the government have clashed over the handling of the police response. The Police Federation said on Monday that Mr Cameron was "wrong" to suggest "back office" police officers could be freed up to increase police numbers on the streets - as many did important roles in child protection and domestic violence units.
Some of the Conservatives' coalition partners have also warned against "knee jerk" responses - Lib Dem deputy leader Simon Hughes has warned against treating rioters in social housing differently to others by removing housing and benefits.