Councillor Gordon Matheson snubbed yesterday's leaders' meeting at the Convention of Scottish Local Authorities, the organisation that represents all 32 of the country's councils, after serving notice to quit in April.
An email sent on behalf of Mr Matheson, seen by the Evening Times, invites Labour colleagues to "move on" and underlines his commitment to working together "post-Cosla".
Mr Matheson also revealed that he informed Cosla chief executive Rory Mair that he has legal advice which cements his position that "no payment will be forthcoming" for liabilities incurred by leaving the organisation.
Cosla has warned that Glasgow and seven other Labour-led councils could face a bill of £3.5million for pulling out. They plan to leave Cosla in April next year in a row over how government cash should be distributed and the cost of membership.
Mr Matheson's email to Labour council leaders reads: "It's safe to assume that no payment will be forthcoming from Glasgow City Council.
"In terms of the future, there have been a number of very positive discussions about how, post-Cosla, councils will cooperate on issues such as policy development and government lobbying."
He concluded his email, which was copied in to Scottish Labour's local government spokeswoman Sarah Boyack, and general secretary of the Scottish Labour Party Ian Price with a plea to put the matter to bed. He said: "I have no intentions of dwelling on what divides us. It's important to move on."
The communication was dismissed by one Labour local authority leader, who plans to keep his council in Cosla.
East Renfrewshire leader Jim Fletcher said: "I don't support the councils that are leaving.
"With 16 Labour leaders, we had control of Cosla and, with the resignations, we've given it away. It's not a particularly clever thing to have done."
Along with Glasgow, South Lanarkshire, Inverclyde, Renfrewshire, West Lothian, Aberdeen, West Dunbarton-shire and Dumfries and Galloway councils all intend to leave Cosla.