The report states the home Office, the DfEE and the department of health need to make funds available to ensure local authorities deliver adequate services.
LGA chair Jeremy Beecham said: 'The Audit Commission report appeals to the Government to resource fully the costs of providing services to asylum seekers, including education and social care.
'The LGA welcomes increased funding announced so far, but will continue to lobby government so that local authorities can properly fulfil their obligations and to ensure this national burden does not fall on the council taxpayer.
The report also highlights the difficulties local authorities face in making complex arrangements for additional and exceptional responsibilities in what is a sensitive area.
However it acknowledges some of the very good work achieved so far by the LGA and some local authorities.
Sir Jeremy added: 'Prior to late 1996 local authorities had no responsibility for asylum seekers. From then until now authorities have coped with more than 80,000 asylum cases.
'The home office is working to take over full responsibility for asylum under its dispersal programme, and the LGA will continue to assist local authorities in supporting the home office to provide decent, cost-effective services to asylum seekers.
'We will be urging authorities to adopt the Audit Commission recommendations, many of which have already been taken up in some parts of the country.
Sir Jeremy said: 'The LGA is lobbying the DfEE for additional money which is urgently needed for education support services like interpreters. A£1.5m fund has already been established to support dispersed asylum seeking children, which the LGA believes is a small step in the right direction.
'The association is also developing guidelines for dealing with asylum seeker children at the request of the DfEE, which we will be issuing to schools as soon as possible.'
In a separate move, the LGA is pleased to announce the North East regional consortia, led by Newcastle City Council, is the first consortia in England to agree in principle to sign a contract with the home office's National Asylum Seeker Support Service (NASS) to provide accommodation for asylum seekers. Once agreed the North East will provide 1,400 units a year.
Sir Jeremy said: 'The North East accommodation contract will be a good step towards securing enough accommodation to ensure asylum dispersal is effective, and to take the heavy burden off authorities in London and the South East.
'The LGA hopes other authorities will sign up over the next few months, and if negotiations remain on course the LGA believes there should be no barrier to NASS taking over responsibility for all asylum seekers on July 1.'