The row was sparked by a letter education secretary Michael Russell wrote to Scotland's councils, asking them not to continue with or bring forward new proposals to close schools until June next year.
However, the head of education at one council told The Scotsman that the move would lead to a 1.5 million black hole in next year's budget, which he warned would have a "big impact" on already "squeezed" services.
Mr Russell wants councils to back the move voluntarily. However, the Scottish Government said it could force councils to comply, if necessary, as it emerged that the education secretary was facing a legal challenge over his refusal to allow a school closure programme in the Western Isles.
Western Isles Council leader Angus Campbell said: "Comhairle is continuing the process of judicial review of those decisions whilst maintaining a dialogue with the Scottish Government." Mr Campbell, who also wants the SNP government to pay to keep the schools open, said the council would also be pressing ministers to suspend any request for a moratorium on closures until after the meeting of local government body Cosla on 24 June.
Meanwhile, Argyll and Bute Council leader Dick Walsh called for "additional funding" to cover a shortfall in the authority's budget due to the suspension of closures.
He said: "If this is a Scottish Government policy, then (Mr Russell] needs to give Scotland's local authorities clarity regarding whether there's likely to be any additional funding which will enable councils to protect their education budgets.
"Argyll and Bute currently has a primary school capacity of some 11,500 pupils, but a primary roll of only around 6,000 pupils.
"This is an unsustainable situation, and one which predictions suggest will get worse in the future if no action is taken."
Bill Fernie, Highland Council's education committee chairman, also appealed to the education secretary for additional funds to cover any shortfall caused by the policy.
He said: "We have pencilled in savings for 2012-13 of 1.5m from a review of our primary schools. If we are not able to make that saving, then we will have to do it from other areas of expenditure. This will have a big impact.
"The 1.5m shortfall is likely to come from the rest of the education and culture budget, which is already squeezed. Given that this is a short-term measure, some short-term finance would be very useful."Cosla president Pat Watters suggested that Mr Russell's move "did not add up" and said he was unhappy about not being consulted before the minister wrote to councils individually.
However, Mr Russell, who has set up a rural education commission to investigate the issue of rural school closures, said rural schools were "fundamental to the social and economic make-up" of many communities.
He said: "To allow for a comprehensive and fair assessment of the closures process, I have asked for a one-year moratorium during which local authorities will not propose rural schools for closure.
"During this period a new Commission on the Delivery of Rural Education will be tasked with, amongst other things, reviewing the legislation and its application and making recommendations on best practice on the delivery of education in rural areas.
"It will also look at innovation and the link between rural education and rural regeneration."