David O'Neill, president of the Convention of Scottish Local Authorities (Cosla), said the difficulties were being caused by Labour-led councils neglecting the cause of the "common good" served by local government.
In his address today at Cosla's annual conference, amid threats and notifications to quit the organisation by several councils, Mr O'Neill will warn tackling inequalities in health, life expectancy, education and employment across the country is being jeopardised by party politics.
Ahead of the meeting, Mr O'Neill, a long-standing Labour councillor, said: "At a time when public confidence in politicians is not high - although confidence in local politicians remains higher than in anybody else - what does it say about us if our way of working is to be consensual up to the point where we don't individually get what we want and spit the dummy out and threaten never to speak to our political colleagues again?
"Whether it is inequality in health, inequality in education and jobs or inequality in that most basic measure, life expectancy, Scotland is still not closing the gap between the best off and the worst off. "
A fortnight ago, Glasgow City Council's ruling Labour administration announced it was leaving Cosla, which it said was being used as a "human shield" by the Scottish Government and exists solely in the interests of a "stultifying and artificial unity".
Several other councils - Dumfries and Galloway, Aberdeen, South Lanarkshire, Renfrewshire and Inverclyde, all Labour-led - have all applied to leave Cosla.
The row centres on issues of where the power lies within the organisation, how funding to local authorities is distributed and the overall effectiveness of the body.
A break-up could affect budgets for services as Cosla negotiates the overall funding package for local government with ministers, as well as wage deals for around 250,000 council staff.
Mr O'Neill added: "Paraphrasing one of JFK's most famous quotes, I would encourage all of you to 'think not what Cosla can do for you but rather what you can do for Cosla'."
However, Gordon Matheson, leader of Glasgow City Council, which is choreographing the departures, said: "Cosla's job is to deliver for its members.
"I don't believe it's doing that and that's why we're leaving."