School budgets are to be stretched by a costly new exam appeals system which can levy charges for every paper reviewed by markers.

The Scottish Qualifications Authority (SQA) has introduced "Post-Results Services" which offers a £10 "clerical check", a "marking review" costing £29.75, or a "priority marking review" at £39.75.

If the grade is changed or if pupils provide medical certificates proving there are exceptional circumstances, there is no charge, but many schools will get bills for thousands of pounds for reviews where the result is unchanged.

A Freedom of Information request reveals two-thirds of Scotland's councils will force cash-strapped schools to pick up the tab.

All 32 local authorities were asked about Post-Results Services payments. Nineteen will ask head teachers to find funds. Twelve said the fees would be met from a central budget. Renfrewshire failed to respond.

The Scottish Conservatives' education spokeswoman, Liz Smith MSP, fears some schools will be less likely to use the new system.

She said: "This is a major concern for parents who rightly want to know any request to review SQA exam marking is done purely on the basis of academic criteria and not because of constraints on budgets … These statistics for the new system show that there is a very mixed picture across Scotland's local authorities. When local authority school budgets are already under very considerable strain, the concern must be that, by passing on costs to individual schools, there is the potential disincentive to ask for too many reviews."

General secretary of teachers' union EIS, Larry Flanagan, said: "It is vital that, in all schools, the decision to appeal or not to appeal is determined purely by the quality of a pupil's work, based on the professional judgment of teachers, and not influenced by any other consideration such as the cost of the process.

"The SQA needs to ensure that the cost of making an appeal does not act as a disincentive to schools, and local authorities must make adequate financial provision."

Local authorities also seem confused over how fees will be met in future. Three councils - Edinburgh, Comhairle nan Eilean Siar and Scottish Borders - have ruled out a move to let parents pay. Others are less clear.

Smith fears pupils from poorer backgrounds could be disadvantaged if parents can meet the cost.

She said: "The local authorities have made it clear they will do everything possible to avoid parents paying the fee but there are some - for example, Glasgow - which have not decided what the future structure will be."

A Scottish Government spokeswoman insisted the SQA "does not accept payment from individual candidates or their parents".

She added: "The new system was introduced to ensure a fairer approach and is based on the professional judgment of teachers and schools. A school should only request a review if it thinks there is a legitimate question."

"How the payments are made is a matter for local authorities with their individual schools."