Cosla (Convention Of Scottish Local Authorities) has been rocked in recent weeks by a series of Labour-led councils who have signalled their intention to abandon the convention.
Councils are divided over the need to present a united front to secure a better deal for local government as a whole and disquiet over a perceived "centralising" influence of the Scottish Government, in particular its commitment to keep council tax frozen.
Cosla president David O'Neill said the convention needs to be both "comfortable with local variation" and present a "cohesive voice" to government. Mr O'Neill, leader of Labour-led North Ayrshire Council, said Cosla plays "a very significant role in working to address inequalities in Scotland".
"To be successful in the short and long term on that important goal only a cohesive and powerful voice for local government across the whole of Scotland has any chance of success," he said.
"Seeking to damage that voice is short-sighted because in the long-term the impact will be felt by those in our communities who we represent and need our support, and they won't thank us if we fail to deliver."
He added: "I have a real concern vitality of local governance is suffering. Local democracy is under pressure in Scotland. It's ailing because it is large-scale, remote and depowered due to centralisation which started in the 1960s.
"We need to not be afraid to do things differently. We need to empower local government fiscally so that real choices can be made about local services and how they are funded."