The leaders on the Convention of Scottish Local Authorities say in their reply to Peter Peacock: "There has been no recognition in the local government settlement of the capital consequences of employing more teachers and reducing class sizes.
"Several councils have expressed a view that some targeted capital expenditure is required to ensure that there is sufficient accommodation to meet the policy objectives."
Mr Peacock has stuck firmly to his intention of employing extra teachers so there are 53,000 in post by August 2007, and of reducing the limit on class sizes to 25 pupils in primary 1 and to 20 in maths and English in S1 and S2.
The Scottish Executive Education Department says that the additional funding announced for the schools fund should be sufficient to cover any costs arising from these pledges. But Cosla argues that the fund is already overstretched and members who were consulted said that it was "already expected to cover a multitude of school estates needs and simply cannot cover everything".
Cosla, which has come under pressure from ministers to ensure that cash to implement Executive policies is not spent on other things, says that unfairness could creep in if councils receive money to reduce class sizes based on the normal grant distribution rules.
"Inevitably, given local policy decisions, some authorities where class sizes are already small would receive more funding than required to meet the reduction in class sizes, and others where class sizes are bigger would not receive enough."
The Executive is consulting Cosla on whether the normal rules for dispensing grant should apply, or whether the resources should reflect actual class size. Councils are insisting that funding should be sent to councils in the normal way, with pupil numbers as the key indicator.