The council is "facing huge challenges" as it battles to plug a £35m budget gap in the next three financial years.
Town hall finance bosses have already identified potential savings of £9.4m which need to be made up to 2028.
But the local authority says that a gap of more than £22m remains with the majority of that sum needing to be found in the first year.
Cllr Sean Thorpe, cabinet member for finance, said: “Once more, we are facing huge challenges in setting the budget for 2025/26.
“This is being caused by insufficient funding, huge increases in costs, and an ever-increasing demand for services, particularly in adults’ and children’s social care which together take up nearly three quarters of the council’s budget.
“We are in the bottom 20 per cent for council funding, and our spending power in real terms has been slashed over the past decade.
"This has let us to find £150m in savings over that period.
“As in previous years, we will have to use reserves to shore up the budget and keep services going, but you can only do this for so long.
“Bury is not alone in this challenge – it’s a serious problem faced by councils across the country, who have been under-funded for more than a decade.
"The only long-term solution is a complete review of the way councils are funded, something that was promised years ago and which we and others have long called for.”
A report outlining the council’s finances is due to be considered at the next cabinet meeting on Wednesday, November 6.
Subject to cabinet approval, a public consultation on the budget proposals will take place between November and January, with residents asked to have their say on how the savings can be made.
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Council leader, Cllr Eamonn O’Brien, said: “In spite of our budget challenges, we have been able to invest in the future prosperity of our borough – the major regeneration projects taking place in Radcliffe and planned for Bury and Prestwich are testament to that.
"This is our home, and we all want to ensure that our borough thrives for generations to come.
“The immediate challenge is getting the money we need to run the essential day-to-day services that people rely on.
“We will do everything to can to keep those services going, but this will involve some very tough decisions, and we have to set a legal budget next March.
“I urge everyone to take part in the budget consultation when it begins next month.”
Bury Conservatives leader, Cllr Russell Bernstein, says his party want to "work constructively" with the council amid the financial challenges.
He said: “I fully appreciate that there are significant funding challenges facing many in local government of which Bury is included.
"I also believe the significant financial challenges in Bury are exasperated by the inability of the organisation to deliver savings in previous years.
"The report being presented to cabinet next week also does not include any of the impact which is likely to be announced in today’s budget (Wednesday) such as fuel duty increases which will only add to the problem.
"Myself and my Conservative councilor colleagues want to work constructively with the administration to ensure we can deliver a budget for the people we all serve.
"In calling for the Labour government to put their money where their mouths have been for a number of years and provide appropriate funding, I was not expecting this to happen as this government to date do not seem to want to prioritise the delivery of local services.”
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