The Convention of Scottish Local Authorities was warned by the committee's convener, Labour MSP Karen Whitefield, that failure to answer MSPs' questions in written evidence, or refusal of future invitations to appear, would result in the committee resorting to its powers to compel attendance.
A Cosla spokesman claimed the authorities' body was the victim of "political in-fighting" and the committee had agreed to let it submit written evidence on this occasion.
The row erupted at last week's education committee meeting, where MSPs heard evidence from Scotland's largest teaching union on its petition for "significant reductions" in class sizes during the lifetime of the next Scottish Parliament.
The Educational Institute of Scotland said that while class-size reductions were a commitment in the new concordat between local and national government, "it does not seem clear the resources are there".
There was "a gap" between claims from Cosla and the Government that the concordat was fully funded, and individual councils' claims they did not have the resources to implement commitments such as reducing class sizes to 18 in P1-3, said the EIS.
"Cosla and the Government say there's enough money, so both appear to be tango-ing," said Ronnie Smith, general secretary. "Talk to any individual education authority and it will tell you how awful the settlement is and the cuts it has to make."
Only two authorities have an unequivocal target date to comply with class-size cuts - Midlothian and Orkney, by the 2010-11 session. Glasgow is refusing to implement it.
The union wants all classes set at 20 from P1-S6 and cited American research on class-size reduction to support its argument. Glasgow University academics claimed it should not be applied to Scotland. "Tennessee is not Scotland; Scotland is not Tennessee," said Valerie Wilson, former director of the Scottish Council for Research in Education, referring to the Tennessee STAR report
- Directors of education said this week the Government's class-sizes policy would cost pound;422 million to implement in just two-thirds of primaries. A survey of 22 councils by the Association of Directors of Education in Scotland found that cutting class sizes to 18 in P1-3 would require 2,173 additional teachers, costing pound;62 million a year, with 900 additional classrooms required at a cost of pound;360 million.