The LGA made the call as it published a report showing that more than 46,000 fewer young people are being helped by national job schemes today than three years ago.
The report shows that in 2009/10, 605,354 young people in England aged 16 to 24 joined a nationally-run employment scheme, including the Youth Contract and apprenticeships, but in 2012/13 the number was 559,183 – a fall of eight percentage points.
The report also said that the way the government publishes results of its national schemes is complex and does not convey how they are helping young people.
Figures published in July suggested the government had made less than 5,000 wage subsidy payments under the Youth Contract scheme in 2012/13, which are offered to employers once a young person has been in a job for six months.
The government anticipated take up to be much higher, having allocated funding for the wage incentive to help 160,000 young unemployed people over three years.
In contrast, the LGA found local authority schemes run over the same period in Leeds, Wakefield and Bradford supported 57 per cent of participants back into education, training or employment.
David Simmonds, chair of the LGA's Children and Young People Board, said local attempts to provide for unemployed young people had been “hampered by successive centrally-driven government approaches”.
“While there are a number of good initiatives, government has sidelined councils and incentivised a series of services like schools, colleges and voluntary sector providers to work in isolation of each other, with no clarity on who is responsible for leading the offer to young people on the ground,” he said.
“This has long been a major frustration for councils, who are in the unique position of knowing the young people in their area and the skills and training required by the local jobs market.
"We would now urge government to give local authorities and their partners the powers to ‘own the problem' and become the link between young people and local employers.
“By introducing a local approach to addressing youth unemployment, councils and their partners will be better able to spot and offer early help to young people struggling at school, train young people in skills to take local jobs in local labour markets, help improve the performance of the Work Programme for the hardest to reach, and target job subsidies to local businesses offering the best opportunities for young people."
Simmonds also called for the government departments to adopt a common system for providing information on their programmes.
Jenny North, director of policy and strategy at charity Impetus – The Private Equity Foundation, backed the call.
“While there are many schemes to help young people get back into work or training, today accessing this information can be confusing and complicated,” she said.
“In the UK there isn’t just one labour market, there are many local labour markets.
“Local agencies and partners know the needs of their community best. We have been calling for a local approach to tackle the problem of getting more young people into work and training.”
North suggested schools could work more closely with local employers to develop city or regional development partnerships to help young people make successful transitions from education to employment or training.
Youth unemployment figures published earlier this month by the Office for National Statistics showed the number of unemployed 16- to 24-year-olds increased by 15,000 in the last quarter to reach 973,000.