Strike action could continue over the next three months, with no further talks aimed at resolving a pay dispute for local authority workers currently planned.
Bins have been overflowing on city streets after refuse workers walked out, while hundreds of schools and early years establishments will close for three days next week.
Unions called for a flat rate pay increase and pointed to a £1,925 deal offered to council staff in England as a template.
On Monday, local authority body COSLA made a fresh offer which included a minimum pay uplift of £1,925, based on a 37-hour working week.
However, the offer was rejected by Unite, who have stated that it remains a minimum of 5% on average across local government pay grades, with a varying one-off payment.
Deputy first minister John Swinney said that he wished the Government “could go further”, however he stated that the deal “does offer significant increases for those on low pay”.
Wendy Dunsmore, Unite regional officer, has argued that the one-off payment will quickly disappear, with the union calling for the money to instead be included in the wages of workers.
Speaking on the BBC’s Good Morning Scotland programme on Tuesday, Dunsmore warned that workers on the lowest pay will be impacted more by the cost of living crisis than anyone else.
“It’s a £1,300 pay rise and then a £600 payment which means that will disappear as soon as they pay their electric bill,” she said.
“It’s not in their wages and that’s what we’re looking for. We’re looking for a pay rise that’s in their wages.
“The higher paid within the councils are getting the consolidated pay so why shouldn’t the lower paid?
“The lower paid are going to be impacted more with the cost of living crisis than anyone else.
“And while COSLA are saying that it’s the best rise in 20 years, or whatever it is, don’t forget that council workers didn’t have any pay rise, they were the absolute victims of the austerity within this country for the last 15 years.”
Dunsmore described the one-off payment as a “sweetener” that would only benefit workers for the month ahead.
“The cost of living crisis is not going away and neither is our workforce,” she said.
“They are determined that they are going to get a cost of living increase for everyone in their pay packets, not just a sweetener for this month only.”
Asked whether the dispute could run into October or November, she responded: “Yep, we’re absolutely resolute that this is going to be a winter of discontent and it will escalate, but we’re hoping against all hope that the Scottish Government and COSLA will see sense and get back round the table with a proper rise for the lowest paid within local authorities.”
Dunsmore urged the Scottish Government and COSLA to get back round the negotiating table.
“There is no rounds of talks yet been organised as far as I’m aware,” she said.
“But we’re urging the Scottish Government and COSLA to get back round the table and take meaningful negotiations.”
Any mediator in seeking to bring a resolution in the dispute would be welcomed, Dunsmore added.
She said: “We will talk to anyone who will get this to an end, we will speak to anyone, we’ll go to any meeting, any time, anywhere.
“And we’ve put that out to the Scottish Government, we’ve put that out to COSLA and we were in talks all over the weekend.
“So, if they want to bring another third party in, well we’ll talk to everyone.”