Key aspects of the McCrone deal are said to be lagging behind because of the failure to take into account the difficulties of rural authorities. Continuing professional development, extra support staff, additional help for probationers and the winding down to retirement scheme for teachers over 56 have all been hit.

Highland says it is pound;6.6 million short over three years and accused Mr Peacock of getting his sums wrong. It believes as a rural authority it is penalised by a funding system based on pupil numbers and not on the actual number of schools and teachers.

But Mr Peacock replied that the formula had been agreed with the Convention of Scottish Local Authorities and took account of the extra costs of serving small schools in rural areas and islands.

“Separate allowances are also made through the special island needs allowance and Gaelic-medium education specific grant. Highland Council benefits from these adjustments by over pound;4 million this year on top of its allocation based on pupil numbers,” Mr Peacock said.

Drew Millar, Highland’s lifelong learning spokesman, said these grants had nothing to do with funding the McCrone package. “They are a separate issue. They were never meant to pay for all the extra staffing and conditions that are supposed to be part of the McCrone settlement,” he said.

“Mr Peacock is also implying that we have got our figures wrong. But Highland is only one local authority among many with remote rural areas that have been affected, including Argyll and Bute and the Western Isles.”

Mr Millar said the implication of the minister’s remarks was that he expected the authority to close rural schools. “How much more evidence does he need before he gives us the extra funding that would allow us to treat our teachers justly?”