The Convention of Scottish Local Authorities (Cosla) said legal obligations will result in the eight Labour-led councils leaving it having to pay out a combined £3.5 million.
But the move has deepened the rift within Cosla, with those departing claiming it has strengthened their resolve to go.
Sources at the country's largest authority said it was disputing Cosla's position and how it would be enforced, adding it believed the organisation was attempting to intimidate smaller authorities into staying.
With the liabilities faced dependent on the size of the individual council, Glasgow alone would face a bill of around £1.2m to leave.
The 32 council leaders were briefed on the situation yesterday by Cosla's chief executive, Rory Mair.
Glasgow's leader Gordon Matheson told Mr Mair he would "see him in court". A statement issued later passed that remark off as a light-hearted comment.
Mr Mair said the legal set-up of Cosla meant those departing were partly liable for the lease of the organisation's Edinburgh headquarters and staff costs.
Several of those authorities leaving Cosla have cited saving cash from membership fees as a motivating factor, while the most recent to join the exodus, West Dunbartonshire, said it was doing so in part over concerns of paying more to be part of the organisation.
Only North Lanarkshire, which has opted to remain within Cosla, made any public reference to ongoing liabilities when discussing it's membership.
Mr Mair told the council leaders: "All the members have to continue to meet these obligations even if they leave or if for some reason something happens to Cosla.
"The law and the constitution state quite clearly that you cannot get out of these obligations just by choosing to leave the collective that is Cosla. Indeed, our own constitution makes it quite clear that contracts like the lease are binding on every member council jointly and severally."
Glasgow, Aberdeen, Renfrewshire, South Lanarkshire, West Dunbartonshire, Dumfries and Galloway, Inverclyde and West Lothian all plan to leave.
The row centres on where the power lies within the organisation, how funding to local authorities is distributed and the overall effectiveness of the body.
Glasgow has claimed plans to change voting structures within Cosla would deny it around £15m and local government could come together "without the need for a separate organisation with its own substantial office and bureaucracy".
Mr Mair said: "The cost for ongoing liabilities we believe are legitimate is £10.736m. The outgoing councils have to meet 33% of this figure which means that from these eight councils a payment of £3.552m has to be made."
Mr Matheson said: "Glasgow, and several other councils have a taken a democratic decision to leave Cosla. It is profoundly undemocratic to use the threat of legal action to try and force them back into the fold.
"I cannot conceive of a set of circumstances where, having given a year's notice and paid a year's subscriptions, the council tax payers of Glasgow could be liable for Cosla's future costs. If they intend to follow through on their threat, we will of course defend our position."
A senior local government source said: "Whether deliberate or not the serving of notice by a group of councils has had a destabilising effect not just on Cosla but on the Scottish local government family. All Rory Mair did was put the facts out there."