The Unite, Unison and GMB unions have suspended strike action planned for next week.
Local government and school support workers had been planning to take industrial action on 14 October in a dispute over pay.
The unions are now going to consult their members on proposals put forward by the LGA last month.
Under the proposals, made by the LGA on behalf of employers, councils will be consulted on proposals to increase pay by 2.2% for the majority of workers. The package also suggested higher percentage increases for lower-paid employees.
Unite said the new offer, which would see thousands of the lowest paid employees getting a rise of up to £1,065 a year from 1 January, would be put to members in a consultative ballot.
Fiona Farmer, Unite national officer, said: “We believe the offer is the best achievable by negotiation, but local government employers and the government should be under no illusions that we will continue to campaign against poverty pay in local government.”
Brian Strutton, GMB national secretary for public services, said: “It has proved extremely difficult to persuade the local government employers to agree new pay proposals for us to consult our members on.
“But now we have an agreed set of new proposals which we will consult on and, while doing that, the GMB is suspending the strike planned for 14 October. We will issue more details about the consultation shortly.”
An LGA spokesman said: “Unison, GMB and Unite have made the right decision in calling off the strike planned for next week.
“It is good news for our employees and for the millions who rely on the services which local government provides, and now gives the employers and the unions time to seek views on the proposals.”
The LGA’s proposal was for a 2.2% pay rise for all staff earning £14,880 and above, with higher percentage increases for those earning less than this. The deal would run from 1 January 2015 to 31 March 2016.
A one-day stoppage in July saw thousands of local government workers walk out across England, Wales and Northern Ireland.