The executive has agreed to write to finance secretary John Swinney ahead of the January 22 signing deadline for clarification on part of the deal that is on the table.
At the centre of its concerns is the impact the decision to direct £250 million of a £400 million increase in health spending to the new health and social care partnerships will have.
Before Mr Swinney’s offer last month, the council had drawn up plans to cut spending by £18 million this year, but the settlement has left the town hall to find almost £7 million more.
Leader of the administration Councillor Craig Martin said: “We can’t accept the package when we don’t have all the facts. We need to have a definitive answer on how this £250 million pot will be distributed and Mr Swinney is the man who can provide it.
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“It would have been much better if the government had offered the £250 million as ‘new’ money instead of taking it from the settlement, but it opted not to.”
His motion that a letter be sent was approved unapposed, but the SNP claimed it is a waste of time.
Councillor Tom Coleman said: “It’s a cheap stunt. The money will find its way back to the council in some shape or form.”
Chief executive Mary Pitcaithly warned: “There has been absolutely no clarity on this issue and there are also other uncertainties. As the council’s chief policy advisor it would be wrong of me not to point out that if that £7 million is not there the council would be in a perilous position. It’s really important we seek clarity because the potential of building a budget on sand is there.”