They say taking kids out of lessons is not “efficient”, with pupils spending two hours out of school for just 20minutes in the water, said a spokesman.
But opponents say youngsters’ lives are being put at risk by SNP cuts. Forty per cent of Scottish kids can’t swim 25 metres.
Dundee City Council said the decision has been taken following discussions with head teachers. It said taking children out of school for lessons was not “efficient”.
The council said schools which want to continue teaching pupils to swim could use Pupil Equity Funding provided by the Scottish Government to cut the attainment gap to pay for lessons.
Lochee Labour councillor Michael Marra said axeing lessons was a “direct result of SNP cuts”.
Sharon Macdonald, director of development at Scottish Swimming said the decision was “disappointing” and that without lessons many children from poorer backgrounds will no longer get the chance to learn to swim.
She said: “It is very disappointing but Dundee is not the first and it will not be the last council in Scotland to do this.
“There is a direct correlation between a pupil’s economic background and learning to swim, so for some children if they don’t learn to swim at school, they won’t learn at all. It is disappointing but we understand the economic pressures councils are under.”
The Scottish Government provided grants to encourage children from disadvantaged areas to learn to swim but this scheme ended in 2015.
Unlike England, there is no obligation to teach children swimming in Scotland.
Ms Macdonald said, as well as health benefits, learning to swim also teaches children about water safety.
She said: “Previous research found 40% of children could not swim 25 metres, which is not great for a country with a lot of open water and lochs.”
Mr Marra said: “Learning to swim is a vital life skill that makes our children safer and healthier. Scrapping swimming instruction in our primary schools is the direct result of SNP cuts from Edinburgh being passed on by the SNP in Dundee.
“Most families have no alternatives and kids will now go without swimming lessons. There is a two-year waiting list for council swimming and that is if you can afford to pay the fees.
“I have real concerns that Pupil Equity Funding could be used to plug the gap.
“That money is meant to be providing additional support for pupils who find themselves in poverty and in need of support to meet their potential.
“If the council is cutting services and trying to raid this pot to replace them only for some pupils then they are making things less equal rather than improving the situation.”
A spokesperson for Dundee City Council said: “Following discussions with primary head teachers it was agreed that swimming lessons for pupils in their current form were not the most effective or efficient way of delivering the curriculum during the school day.
“In some cases a class could be out of school for up to two hours and only have 20 minutes in the pool. Head teachers have been given the opportunity to explore how swimming lessons can be delivered through the Pupil Equity Fund and Leisure and Culture Dundee’s Family Swimming Initiative.”