Councils have called on the Scottish Government to provide extra funding in future budgets to allow them to deliver on its public sector pay policy without cutting services.
Ministers announced an end to the pay cap for public sector workers as part of their 2018/19 tax and spending plans.
A budget deal with the Scottish Greens means pay rises will now apply to 75% of those employed in the public sector.
The Greens' deal also won an additional £170 million for councils.
However Cosla said pay remains a major issue for local authorities.
The council umbrella group's resource spokeswoman Gail Macgregor said: "We acknowledge the additional resources secured into the settlement for this year following extensive lobbying by Cosla.
"However this will not negate all of the challenges we still face, the main one obviously relates to pay for our workforce now that the Scottish Government has set out its public sector pay policy.
"This additional resource has to become built into the core of our budgets for future years."
She added: "This year's deal means Scotland's councils are far from out of the woods and not cementing this funding into core budgets would be an extremely bad result for the delivery of essential services.
"Because quite simply with no money in the settlement from Scottish Government for pay, any pay rises for council workers can only come from cuts to services or council tax rises."
Finance Secretary Derek Mackay said: "In spite of continued UK Government real terms cuts to Scotland's resource budget, we have treated local government very fairly. In 2018-19 councils will receive funding through the local government finance settlement of £10.7 billion.
"This will provide cash terms increase in funding for local revenue services of over £174 million - a 1.8% rise, and capital spending of £89.9 million - an increase of 11.4%. This delivers a real terms boost in both revenue and capital funding.
"As well as this increased funding, Councils have the flexibility to increase council tax by up to 3%. Taken together, this will mean that Councils have access to an additional £251 million that can be spent at their discretion, including on pay increases for their staff."
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