Sir Sandy Bruce-Lockhart, chairman of the LGA, this week called on all councils to review their procurement practices and offer three-year deals.
"All councils should routinely address three-year contracts to allow the voluntary and community sector to plan ahead," he said.
"Compacts with the sector have been helpful, but more needs to be done to release the potential of these organisations."
The LGA plans to run a campaign later this year to check whether its members are complying with the demands, which were outlined last week in its report Closer to People and Places.
"It's the first time we've ever had such an explicit statement on contracts from the LGA," said Stephen Bubb, chief executive of Aveco, who has heavily criticised short-term contracts.
"Given that 92 per cent of our members have one-year contracts, three years would be significant movement. But why only three years? Seven or 15 year-contracts could be more appropriate in some areas."
Kevin Curley, chief executive of the National Association of Councils for Voluntary Service, said his enthusiasm was tempered by the three-year limit, particularly as his organisation had just moved to five-year Home Office contracts.
He added: "The LGA should name and shame councils that ignore what their chairman says."
Dawn Roberts, head of strategy at Hull City Council, which introduced three-year contracts in its sector funding strategy in March, said councils had realised one-year contracts weren't fair. But she said five-year deals were unrealistic.