An emergency meeting of council leaders in Scotland was held on Friday after the Scottish government announced the plans, but refused to provide extra funding.
Sixteen of the 32 authorities in Scotland said they would need extra resources above funding already agreed between the Convention of Scottish Local Authorities (COSLA) and the SNP.
The move to offer free school meals came as an evaluation of a six-month, £5m pilot scheme, which ran across five local authorities and covered 35,000 children, found that the pilot had significantly boosted the uptake of free school meals.
COSLA called the meeting after 16 councils, including Edinburgh and Glasgow, said they could not afford the policy.
However, first minister Alex Salmond said that funding had already been provided in the Concordat.
Speaking after the meeting COSLA president Pat Watters accepted that funding had been included in the settlement for a roll out of free school meal provision.
But he added, ‘In common with all other local government provision this policy is now taking place in a very changed financial and economic environment. COSLA will be making use of the commitment in the Concordat which provides a mechanism for joint discussions with our partners in government regarding the local government settlement to decide how we jointly respond to emerging and exceptional funding pressures.'