The finding is contained in a survey of attitudes towards local authority funding and org-anisation by pollsters Ipsos Mori for the newly formed Commission on Strengthening Local Democracy, established by local council body Cosla.
The council tax has been frozen by the SNP government since it came to power in 2007 and was a pledge of opposition parties at the last election.
But the freeze now costs almost £500 million to fund and as budgets continue to fall, some council leaders have demanded the freedom to raise council tax.
The poll also found that fewer than half of Scots believe vital community services are getting the funding they need, as councils face an increasing cash shortfall in the climate of austerity.
More than 54 per cent of people believe that central government now has more control than it did in the past over local services – and eight out of ten Scots want more say.
Cosla president David O’Neill, who heads the Commission on Strengthening Local Democracy, said the findings are about “starting a debate”.
“We are breaking new ground by offering a mature and evidence-based debate about the kind of democracy we want, regardless of the outcome of the referendum in September,” he said.
“We want to deliver real change and we want to influence change elsewhere.
“But it is hugely encouraging that both our call for evidence and our polling work are already showing that, right across the country, there is a growing appetite for a serious discussion about why local services and local accountability matter and how we strengthen them in Scotland’s future.”
Scotland’s councils are facing a dramatic real-terms fall in their funding for local services.
This will decrease by about £350m in 2014-15 to £6.94 billion, before falling by another £279m in 2015-16. But capital spending on building projects is rising by £236m over these two years.
Only 49 per cent of Scots think councils have enough money for the services needed in communities, according to the poll of 1,006 adults carried out by Ipsos Mori. Social care cuts have prompted widespread concerns, while recent figures show class sizes are rising as teacher numbers fall.
On launching the commission last autumn, Mr O’Neill indicated that the freeze on council tax rates in Scotland was not sustainable and warned that new forms of taxation may have to be looked at to plug growing gaps.
The SNP is adamant its flagship policy of the freezing of council tax rates is essential to support hard-pressed families who face crippling rises in the cost of living.
But anti-poverty groups such as the Joseph Rowntree Foundation have warned that better-off, middle-class families are the biggest beneficiaries of the freeze and Labour already has a commission looking into its long-term sustainability, along with other universal services.
A Scottish Government spokesman said councils are “critical” in delivering a range of services that really matter to the people of Scotland.
“That’s why the Scottish Government has fully funded the council tax freeze for the last six years, providing much-needed financial relief to some of the vulnerable groups identified in this survey, such as pensioners,” he said.
“This fully funded freeze is ensuring there no detrimental effect on the level of service provision, and there is a commitment to continue this for the lifetime of this parliament.”
A spokesman for local government minister Derek Mackay said: “The council tax freeze is a popular policy, one which was in the SNP’s manifesto, and which people voted for.”
The SNP government insists that the council tax freeze is fully funded, but its £70m annual cumulative cost means it will cost £490m in the next financial year 2014-15.
Labour MSP Sarah Boyack said: “This poll shows a clear rejection of the SNP’s centralisation of local services.”
Liberal Democrat MSP Alison McInnes said: “The results of the survey articulate what I and many Lib Dems have been saying for years: local decisions should be taken by those in the community for the benefits of the community. Local democracy needs to be strengthened.”