Council tax bills in England must increase by "substantially" less than 5% next year, the government has said.
Some councils are struggling to fund services, the LGA says
Local Government Minister John Healey pledged an above-inflation rise in central government funding for councils over the next three years.
He said the increase would be 4% for 2008/09, 4.4% the following year, and 4.3% for 2010/11.
The Local Government Association said this was not enough to prevent council tax rises being higher than last year.
The deal was "the worst settlement for a decade", according to the association's chairman, Sir Simon Milton.
"Many council leaders will be scratching their heads as they try to work out how they will deliver even better services for local people with less money than in recent years and with greater demands on services."
But Mr Healey told the House of Commons: "Keeping council tax under control remains a high priority for this government.
"We expect the average council tax increase in England to be substantially below 5% a year.
"We will not hesitate to use our capping powers to protect council tax payers from excessive increases. This is a tight settlement but it's fair and affordable."
The funding settlement will take total central government funding for councils to £76.7bn by 2010/11.
Last year's average council increase was just over 4% on average.
Shadow local government minister Alistair Burt, for the Conservatives, said the settlement would mean an extra £208 on council tax bills for those in the average band D - a "whopping increase" of 122% under Labour.
"This pushes council tax at Band D through the £1,500 barrier by the next general election," said Mr Burt.
He added: "This statement is a cunningly worded invitation to reduced services from councils and higher bills for taxpayers."
Mr Burt also said: "From young to old, especially those in receipt of elderly care and those paying council tax, today's statement marks a further chapter in the long, slow but certain betrayal of people's hopes and expectations from this government."
Mr Healey's statement would have been heard with "more than disappointment" in town halls up and down the country, he added.
For the Liberal Democrats, Tom Brake said there were "no surprises just bad news" in the statement.
The government had not taken the opportunity to reform council tax and replace it with a tax based on people's ability to pay, he said.
"The most unfair tax of all remains in place."
Mr Healey replied that the vulnerable were protected by council tax benefit but that was not true of Lib Dem proposals for a local income tax.
The Local Government Association argues that there are pressures on budgets, with some councils having to ration care for the elderly so that only those whose needs are substantial or critical will get help.
It also cites the increasing cost of waste disposal, with landfill tax rising sharply in the next three years.
"My predictions is that council taxes will on average go up higher than last year," Sir Simon said. "Last year was just over 4%. This year it will be probably around 4.5% on average.
"That will mask variation in some parts of the country there will be lower increases."