Susan Aitken said schemes to support businesses and third sector groups were also in “serious jeopardy”.
Labour, she added, had “cocked this up”, reports our sister title The Herald.
But the Scotland Office insisted the city was set to be better off and claimed the council had been using money meant for communities to fill the gaps caused by underfunding by the SNP government.
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The new Local Growth Fund (LGF) replaces the UK Shared Prosperity Fund (UKSPF) which was initially brought in by the Tories as replacement for EU structural funds lost after Brexit.
For decades, authorities had used the money to support employability, economic development and regeneration, particularly in areas of long-term deprivation.
On Thursday, Scottish Secretary Douglas Alexander said the UK Government would invest £140 million in five Scottish regions to spur on economic growth.
Edinburgh is in line for £37.8 million, the Tay Cities region £19.5, Ayrshire £11.8 million, and Forth Valley £9.8 million.
Mr Alexander said Glasgow would receive £60.9 million.
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However, over the past three years, the SPF has delivered £91 million to the Glasgow City Region.
Cllr Aitken said: “At best, the Labour Government has cocked this up. You can’t talk about jobs, growth and prosperity on one hand yet remove the funding already delivering this with the other.
“We’ve many crucial and successful programmes and organisations doing an incredible job for the people, communities and economy in every part of the City Region. But the LGF puts that work in serious jeopardy.
“Labour ministers and MPs cannot look city region residents in the face and say they’re serious about tackling unemployment, boosting living standards and supporting local growth while gutting the very funding delivering that.”
As well as the cut in cash, Cllr Aitken said she was also concerned about new restrictions on how the money can be spent.
Under the Shared Prosperity Fund, most of the money was revenue funding which meant it could be used on day-to-day spending.
But under this new fund, that will fall to 30% – a drop from almost £66.5 million to just over £18 million.
Cash will also reduce year-on-year, with a revenue budget of just £4.8m across the entire city region in the third year – half of what Glasgow alone received under the Shared Prosperity Fund in the current financial year.
Cllr Aitken said: “UK ministers have been doing the rounds trumpeting the LGF as new money which will deliver new infrastructure. It isn’t. It’s existing funding, reduced, repackaged and restricted.
“I’m always supportive of new capital funding but UK ministers need to explain why they’re redirecting money away from where it’s proven to deliver jobs and growth.”
She added: “The fact there’s still no clarity on what the rules of the funding will be suggests this hasn’t been fully thought through. If that’s the case my door remains open to anyone in the UK Government for how we fix this mess.”
The UK Government rejected the claim that Scotland is losing out overall, insisting that the Local Growth Fund must be seen alongside three other new schemes.
They said support for local and regional projects in Scotland would be worth more than £2 billion over the next decade.
On Radio Scotland on Thursday, Mr Alexander said the old SPF was being used by the local authorities across the country to “fill the gaps” caused by underfunding from the SNP government.
“We’ve taken a different approach. We’ve given a record settlement to the Scottish Government and we challenge them each and every day to say, frankly, why have we given you a record settlement and yet services are getting worse, not better?
“And at the same time as giving the Scottish Government the largest settlement since devolution, we’re also increasing the direct funding by the UK Government, and I make absolutely no apology for the fact that we are stepping in where the Scottish Government frankly over many, many years has deprioritised the regional economies of Scotland.”
A UK Government spokesperson said: “The Local Growth Fund is just one element of the package of new UK Government programmes to drive growth and regenerate communities across which Glasgow City Region is getting more than £103 million. This means it will be up to £15 million better off than under the UK Shared Prosperity Fund in 2025/26.
“General funding for council services is a devolved matter and should be coming from the Scottish Government and not the UK Government.
“We have provided the Scottish Government with the largest Block Grant in the history of devolution, including an additional £11 billion since the general election, which they should be passing on to local councils in Scotland to spend on improving public services, securing economic development and raising living standards.”