Class sizes in Scotland will not be cut to 18 for P1 to P3 pupils, by the next election, Scotland's most senior councillor has told BBC Scotland.
Ministers said they expected councils to make progress
Pat Watters, who negotiated the local government budget deal with ministers, said it would not deliver the SNP manifesto pledge in full.
But Education Secretary Fiona Hyslop insisted that the government would drive down class sizes.
She added that the pace of delivery could vary across different councils.
Mr Watters, president of local authority umbrella group Cosla, told BBC Scotland's Politics Show that councils would not get any more money to cut class sizes and that there was no progress target.
He said his understanding was that reductions would be delivered in "general terms", adding: "There will be areas in Scotland where the progress is very slow, there will be areas in Scotland where the progress is quite quick."
Mr Watters said of the class size pledge, contained in the SNP government's budget document: "It won't happen within the life of this parliament.
"There will be significant progress made within the life of this parliament, but it won't be completed within the life of this parliament."
Mr Watters, who is a member of South Lanarkshire Council, said: "There's no money in the deal for this. We will use the demographic shift in Scotland to deliver this. That's part of the deal that we've done.
"Where there's no falling school roles, there's no expectation that those authorities will have to go to 18."
But Ms Hyslop said there would be steady progress on cutting class sizes, beginning in more deprived areas, while pointing out that councils would now be allowed to spend their own efficiency savings.
"The most important thing is that this government will drive down class sizes in P1 to P3 and many of them will get down to 18," she said.
"I recognise that we are going to make significant progress on that."
The education secretary went on: "We expect every local authority to make progress in cutting class sizes.
"The pace and scale of it will vary from one local authority to another."
Labour education spokeswoman, Rhona Brankin, said Mr Watters' comments showed the government's class size policy was in disarray, adding: "The SNP have let down Scotland's parents, pupils and teachers, on their promise to cut class sizes."
Liz Smith, the Conservative schools spokeswoman, said: "This is the final nail in the coffin as far as the SNP's commitment on class sizes is concerned.
"It now falls to the SNP to apologise to parents, teachers and pupils across Scotland for the cynical manner in which they have misled them."