More than half of people given ASBOs do not obey them
Home Secretary Alan Johnson has said claims by the police that they should not deal with certain cases of anti-social behaviour were "ridiculous".
Announcing new targets for dealing with offenders in England and Wales, he said action could not be left to councils.
Referring to recent comments by an officer in the Fiona Pilkington case, he said some officers had a "mindset" that the issue was not one for them.
The Police Federation said adequate resources were needed to tackle it.
The organisation, which represents rank-and-file officers, said ministers had launched a string of initiatives on anti-social behaviour requiring police time without considering the "negative impact" these could have on other police responsibilities.
Public outrage over the death of Fiona Pilkington, who killed herself and her daughter in 2007 after suffering years of abuse from youths on her street, has galvanised all the political parties to refocus their sights on anti-social behaviour.
Asked about the Pilkington case, Mr Johnson criticised comments made by an officer from the Leicestershire police force at the inquest into her death that low-level disturbances were better left to councils.
"A police officer saying at the inquest that anti-social behaviour is no longer a police matter, it is for local authorities, it is ludicrous and ridiculous," he said.
"It is just totally unexplainable how a police officer could feel like that but it suggests there is a mindset there."
The Pilkington case showed the need for police, councils and landlords to work more closely together, he added, to identify those at risk and to use existing sanctions consistently against troublemakers.
But the Police Federation said getting to grips with anti-social behaviour was not simply a policing matter.
"All agencies, whether it is the local authority, schools and parents, must play their part," said its chairman Simon Reed.
"To start, what is needed is a zero-tolerance approach, with sufficient police officers on the streets to tackle anti-social behaviour and a criminal justice system that actually does something about these offenders when we bring them to justice."
Amid concerns about flagrant breach of anti-social behaviour orders (Asbos), Mr Johnson said there would be a "clear expectation" of legal action against people who break asbos.
The home secretary has admitted the government eased up on the issue after a period of "intense activity" in the first half of the decade and that progress had "stalled" in recent years.
But he insists the answer is not to pass new laws but to ensure existing powers are used effectively. He is to write to all police forces and councils urging them to use all the powers available to them, including the power to disperse troublemakers and close down premises.
By March, police and local authorities will be required to reply to all complaints about anti-social behaviour, to tell residents what is being done and to explain if problems cannot be addressed.
Ministers are also proposing a new network of victim and witness champions to provide support for victims and assist those willing to give evidence against offenders in court.
Among measures proposed by the Conservatives are "instant punishments" for minor troublemakers and a levy on late-night alcohol sales to tackle drink-related disorder.
The Lib Dems said the government should focus on the basics of law and order, such as more police and a new approach to sentencing, rather than "gimmicks".