Non-teaching staff who are members of Unison rejected the latest pay deal, which would have seen a rise of 67p an hour or 3.6%, whichever was higher, with the deal later imposed on staff.
The union was the only one of the three to reject the offer and, in a bid to put pressure on the Scottish Government, which has repeatedly said there is no money left for improvement, chose John Sweeney’s constituency of Perthshire North for strike action.
The disruption began last week, with all primary schools and daycares closed, and while some have reopened, the majority have not.
In a letter to Perth and Kinross branch secretary Stuart Hope, the First Minister pressed for a solution but the union said Mr Sweeney “should be talking to us, not at us”.
“I very much hope that Unison will continue a meaningful dialogue with local government and join colleagues from the GMB and Unite in accepting the proposal and ending the strike action,” Mr Swinney said.
The First Minister also reiterated his disappointment that the action was aimed specifically at his constituents, describing the move as “totally unfair”.
Last week members protested outside Mr Sweeney’s constituency office in Blairgowrie, Perthshire.
Speaking about the funding of another proposal to Unison members, the First Minister pointed to the dire financial situation.
“While the Scottish Government has no formal role in these pay negotiations, we have taken extraordinary decisions in a challenging financial context to identify an additional £77.5m to support local government pay,” he wrote.
“It is at the absolute limit of affordability and there is no more funding available from the Scottish Government.
“This additional funding has enabled the local government to make an improved offer which will allow the lowest paid workers, including those involved in strike action in Perth and Kinross, to receive a 5.63% increase.
“As well as prioritizing the lowest paid, this offer is also better than the offer made to local authority staff in the rest of the UK and as such delivers what Unison, GMB and Unite have jointly asked for from councils -early in the year.’
Responding to the First Minister’s letter, Unison Scotland’s head of local government David O’Connor said: “These are warm words, not meaningful action. The Scottish Government is ultimately responsible for the costs and must play its part in resolving the dispute, along with (the council’s umbrella body) Cosla.
“Mr Sweeney can’t just pretend it has nothing to do with him or his ministers. The Prime Minister should be talking to us, not at us.
“Closing schools is the last thing staff wanted to do, but staff need a better pay offer that is in line with other public services.
“The strike is the only opportunity left to these workers to show the overwhelming strength of their feelings.”