It wants to prevent a backlash against Muslim and Asian communities and to tackle fears of growing racial tension - attacks on mosques in Liverpool, Leeds, London and elsewhere followed the 7 July bombs, while the Muslim Council of Britain has received more than 30,000 hostile emails.
The LGA wants councils to team up with religious leaders to help police promote anti-hate crime laws. The association has proposed a 'tension-monitoring group' and 'reassurance meetings', in which community members will be able to express their concerns.
It is also asking councils to publicise their work on monitoring racial tension and to work closely with their local media to promote a positive view of ethnic diversity.
Council chief executives and comms staff will be targeted via local government trade press and newspapers, as well as directly.
Plans for future multi-faith community projects will soon be published jointly by the Home Office, the LGA and related groups.
'We are advising councils to monitor community tension. It is important to reassure ethnic minorities that they play an equal part in our society,' said LGA director of strategy Oona Muirhead.