Council chiefs will increase their pay offer to workers to 5 per cent - if the Scottish Government stumps up the cash.
Local authority umbrella group COSLA ramped up the pressure on Ministers amid a threat of crippling summer strikes.
Council staff across the country are being balloted for industrial action over a standoff on pay.
Three trade unions - GMB, Unite and Unison - rejected the 2 per cent offer made by council employers.
NHS staff and train drivers are being offered 5 per cent and the unions want more than is on the table.
COSLA are sympathetic to a bigger rise, but they have blamed the Scottish Government for local authority funding pressures.
A meeting of COSLA last week led to approval of an amendment proposed by the SNP’s Susan Aitken, who is the leader of Glasgow council.
It mandated the organisation to make a “revised pay offer of 5%” which is “contingent on additional funding being provided by the Scottish Government”.
Councillors agreed to “make clear to Scottish Ministers” they must “provide additional financial resource” for councils to protect local services and current staffing levels.
It comes after a row broke out over COSLA claims that an inflation-linked rise of 10 per cent, without extra Government MONEY, could risk 20,000 jobs. Unison dismissed the claims as “blackmail”.
A council source said a 5 per cent increase with nothing extra from Nicola Sturgeon could jeopardise 10,000 posts.
Scottish Tory MSP Miles Briggs said: “Even Susan Aitken has to admit how underfunded Scotland’s councils are under the SNP-Green coalition.
“Cosla are right to press Ministers for a fair deal.
“Local authorities are on their knees and Kate Forbes has signalled it’s only going to get worse. This is despite the Scottish Government getting the biggest block grants in the history of devolution.”
A Scottish Government spokesperson said: “While the Scottish Government is not involved in local government pay negotiations,we note this resolution from COSLA. Pay settlements for council workers – excluding teachers – are a matter for COSLA and are determined through negotiations at the Scottish Joint Committee (SJC).
"As it is not a member of the SJC, the Scottish Government cannot intervene in pay negotiations, which are for the trade unions to negotiate with COSLA.
“Council staff play a crucial role in our communities as we rebuild the economy following the pandemic. We would encourage the parties to maintain dialogue and stay at the table to reach agreement.”
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