The issue is threatening to create a new nuclear split within the SNP, following disagreements over the party leadership's move to end its decades-long opposition to membership of the Nato nuclear weapons alliance.
An expert report due to be published today by the 10-strong group of nuclear-free councils in Scotland says ministers are wrong to let the nuclear reactors at Hunterson in North Ayrshire and Torness in East Lothian keep running for two more decades.
The nuclear-free group includes two SNP-led councils, Dundee and Perth and Kinross, plus Edinburgh, which is ruled by an SNP/Labour coalition.
The report says: "There is no need for the Scottish Government to support risky life extensions."
It concludes that improved energy efficiency, combined heat and power schemes and renewables could ensure that Scotland met its energy needs.
Report author Pete Roche, a policy adviser to Scotland's nuclear-free local authorities, added: "Milking Scottish reactors dry is another way of maximising the chances of an accident as these reactors get older and more decrepit.
"Clearly SNP activists who have been promoting a nuclear phase-out are not going to be happy about the possibility of Scotland remaining nuclear until 2033 and beyond."
Scottish ministers have repeatedly said they will not oppose plans by French nuclear company EDF to apply to UK regulators to keep Hunterston going until 2021. EDF is also likely to try and postpone the closure of Torness from 2023 to 2033.
The dissent within the SNP comes as First Minister Alex Salmond faces a growing revolt over plans to drop the SNP's historic opposition to Nato, with at least seven MSPs joining a campaign to keep the policy.
According to the report, the Hunterston B nuclear station is already older than most of the reactors shut by the German government after the Fukushima disaster last year. Germany also plans to cut electricity consumption by 10% by 2020, while Scotland is expecting a rise of 10%.
The report was welcomed by the SNP councillor for Dunfermline South, Brian Goodall, who also chairs the nuclear-free local authorities in the UK. It showed the Scottish Government how to "dramatically scale up" its visions on energy efficiency and renewables, he said.
The Scottish Government reiterated its opposition to building new nuclear power stations, but a spokeswoman added: "We have made it clear that, subject to the relevant safety cases being made, the Scottish Government would not oppose operating life extension applications at Torness and Hunterston."