The funding announced in the Scottish Budget could lead to councils failing to meet their legal duties and "substantial reductions" in teacher numbers, it has been claimed.
Fears have also been expressed about the impact on additional support needs (ASN) and social care.
In spending plans announced last week, public finance minister Kate Forbes said there would be an extra £494 million for local authorities.
But council umbrella body Cosla said this would effectively be a cut of £95 million once local authorities have delivered Scottish government commitments worth £590 million.
Scottish Greens co-leader Patrick Harvie told Ms Forbes at an evidence session in the Scottish Parliament today that councillors he had spoken to have "serious concerns that councils will be in breach of their legal duties".
School funding fears
He said local authorities would need real-terms funding "stability at least" – on top of additional funding for Scottish government initiatives such as the 1,140 hours of free childcare to be in place by this summer – if core functions are to continue to be carried out.
Mr Harvie added: "I'm sure I'm not the only person around this table who has been told by local government colleagues that the kind of choices they and their colleagues are going to be faced with in the coming weeks will result in substantial reductions in core services – teacher numbers, additional support for learning, social care.
"They have serious concerns that councils will be in breach of their legal duties as a result of choices that they will be forced to make as a result of the current situation."
Ms Forbes fielded questions from MSPs on the Finance and Constitution Committee. She was drafted in to take over the Budget process last week following the resignation of former finance secretary Derek Mackay, after revelations about unsolicited messages to a 16-year-old boy.
Scottish Labour MSP Neil Bibby told her today that the level of funding for local government was "obscene", citing an increase in the Scottish government's capital budget from Westminster.
The minister repeatedly said, in response to Mr Harvie and Mr Bibby, along with Conservative finance spokesman Murdo Fraser and Labour MSP Sarah Boyack, that Scottish government initiatives being taken forward by councils would satisfy local authority priorities.
She said: "In terms of the settlement for local government, as I said on Thursday, there's a cash increase and there's a real-terms increase going into local government in the resource budget.
"What's key is that core settlement includes funding our commitments around early learning and childcare, in terms of £201 million of revenue and £121 million of capital.
"It includes funding our commitments on teachers' pay – £156 million – and also on pensions."
Ms Forbes accepted there were "challenges" being faced by councils.
She said the deal was "a fair settlement", adding: "Nobody is pretending this is an easy process. There are hard decisions across the board.
"But I still strongly believe that we have protected local government and supported them to deliver the responsibilities that we deliver in partnership."
The process for passing the Scottish government's spending plans has been accelerated due to a delay until 11 March in the UK government laying out its Budget.