Elements of the proposal deal were described as "unacceptable" and "shameful" by at least one union. Cosla, which represents local authorities, said the offer – which also includes a Scottish Local Government Living Wage of £7.50 per hour – was final.
The final offer came after Unison, Unite and GMB union delegates met employers on February 5 to negotiate a pay settlement for more than 300,000 council workers in Scotland. All are expected to ask members their views in a full postal ballot.
Unison, Scotland's largest trade union representing 160,000 public-sector members in Scotland, has said a refusal to give a Living Wage annual guarantee or to scrap lower pay rates was "unacceptable".
And they described as "shameful" a refusal to negotiate over a request to allow all public-sector workers to receive annual £250 payments if they earn £21,000 a year, rather that some.
Officials for Unison, Scotland's largest trade union representing 160,000 public-sector staff in Scotland, said they were disappointed with the offer and a that delegates' meeting on March 15 would decide whether to recommend members accept the deal.
Unison also wanted a guarantee that the Living Wage would increase across all of Scotland's local authorities annually. But employers said it was to be left to individual councils to decide, based on their own situations.
Dougie Black, joint trade union side secretary for Unison, said: "We welcome the fact that the employers have gone some way to addressing low pay by the introduction of a Living Wage. This has been a key component of our pay claims for the last few years. However, we are disappointed at the level of the offer at 1%.
"This has to be seen in the context of local government workers only having seen pay increase by 0.65% over the last three years, while many other public-sector workers earning under £21,000 have received an annual payment of £250.
"And of course the cost of living has gone up, with big energy and food price increases."
The inflation rate, as measured by the Consumer Prices Index, was 2.7% in January.
Council staff represent just fewer than 60% of all workers in the devolved public sector, and have borne the brunt of job cuts.
In November, 2011 hundreds of thousands of public-sector workers walked out over proposed changes to pensions, resulting in demonstrations and pickets.