Local government leaders are meeting on Friday, with the prospect of strike action by workers high on their agenda.
Wendy Dunsmore of the Unite trade union said more action could be announced next week unless a new offer is put on the table – adding it wants a £3,000 a year pay rise for workers.
The three unions representing local government workers – Unite, Unison and the GMB – have rejected the 2% pay rise offered.
With the cleansing staff in Edinburgh set to strike between August 18 and 30, Ms Dunmore said the action will mean “the streets of Edinburgh are messy, there is going to be no litter picked up”.
She told BBC Radio Scotland’s Good Morning Scotland programme: “It’s not just Edinburgh, other councils will be going out on strike and there will be announcements next week on that.”
But she said “there is an out for this”, insisting workers “don’t want to go on strike”.
She said: “If the Scottish Government would give money and if Colsa would increase the offer we can stop that.
“The Scottish Government hold the purse strings to Cosla, the Scottish Government finances local government, so the Scottish Government can step in.
“They’ve done it in the past for teachers, they’re doing it for the NHS, they are doing it for ScotRail, so they can step in for Scottish local government.
“They have starved local government of funding for the last 10 years, they have cut year-on-year the budgets, that’s why councils can’t afford to pay their staff.
“It’s now time for the Scottish Government to take responsibility and pay Cosla and give proper funding to the councils, so the councils can give their staff a good recognition and thank them for the good job that they do.
“Our claim is £3,000 for everyone – that is whether you are on £20,000 or £60,000.
“The Tory Government in England has managed to give £1,925 to local government workers, we would have expected more than that because we would have expected the Scottish Government to beat the Tories.
“But we are looking for a substantial increase. We’ve not had a decent pay rise in 15 years. We have got workers who are earning less than they did in 2007 doing the exact same job. That is unacceptable.”
Business minister Ivan McKee told the BBC: “What I can say is the Deputy First Minister John Swinney is in very constructive conversation with Cosla on this matter and we’re hopeful we’ll make good progress there.
“While it’s a matter for local authorities as an employer we are very much engaged in the process and as I say there’s some very constructive conversations happening as we speak.”