During the pilots, the take-up rate in primaries one to three rose to 75%
Labour has claimed that councils are in "open revolt" over the Scottish Government's free school meal plans.
Five to seven-year-olds will get free meals from 2010 but no new money will be given, with funding instead included in the local government settlement.
Labour said 12 of the 32 councils had expressed concerns about how they would finance the scheme.
But First Minister Alex Salmond accused Labour councillors of playing party politics with the government's policy.
Mr Salmond said councils knew that if free meal pilots were successful the policy would have to be funded as part of the existing local government settlement.
Ministers had previously run a £5m trial, giving primary one to three pupils in five council areas free school lunches.
The concordat deal with local councils had agreed that if the trial was a success, legislation would be brought in to make sure all youngsters in primary one to three were entitled to free school meals from August 2010.
During the pilot, the number of youngsters in primaries one to three who ate school lunches rose from 53% to 75%, with Education Secretary Fiona Hyslop stating it had been "a success with pupils, parents and schools".
However Labour said it could cost councils up to £50m a year to provide the service.
The party's education spokeswoman, Rhona Brankin, said: "Fiona Hyslop's credibility is in tatters.
"She has provoked an open revolt from local government, who are being asked to foot the bill for free school meals.
"I am demanding a guarantee that SNP ministers will not penalise councils who are unable to afford this."
The councils expressing concerns about the funding include Edinburgh, South Lanarkshire, Clackmannanshire and North Ayrshire, Moray, Angus and Falkirk.
Senior councillors from Inverclyde, North Lanarkshire, Highland and East Dunbartonshire councils have previously voiced concerns.
But the local government body Cosla has welcomed the policy and said funding was included in the overall local government settlement.
The first minister told BBC Scotland: "It'll cost £28.6m, assuming a 70% take-up rate, not some of the bigger estimates we've seen elsewhere.
"In return for a record settlement, the councils agreed to a range of things that they would implement, including - if the pilots were successful - free school meals for primaries one to three.
"There's huge enthusiasm in many councils to get on with it and the ones that are kicking up a fuss are doing it for political reasons.
He added: "It's a case of the Labour Party quite literally wanting to take food out of the mouths of children and I don't think the public is going to stand for it."