Glasgow's Gordon Matheson said the impact of the Offensive Behaviour at Football Act had been to drive a wedge between fans and the police, accusing the legislation of demonising supporters and calling for an immediate review of the law.
The legislation gives police and prosecutors new powers to tackle sectarian songs and abuse at and around football matches, as well as threats posted on the internet or through the mail.
It created two distinct offences, punishable through a range of penalties up to a maximum five years in prison and an unlimited fine.
An agreement was reached for the Scottish Government to review the operation of the offences after two full football seasons and to report back to Parliament one year later. Concerns have since been raised by fans about police tactics and the act in general.
In a letter to Roseanna Cunningham, Minister for Community Safety and Legal Affairs, Mr Matheson said: "My administration is committed to promoting the overwhelmingly positive side of football in Glasgow. I do not believe this vision is irreconcilable with the Scottish Government's original intentions, before this legislation went badly wrong.
"Rather than ameliorate the issue of sectarianism, this Act has had the perverse effect of creating an air of mutual antagonism between the police and supporters. I strongly urge you to initiate an immediate review of this legislation."
But one Scottish Government source said: "Why is he saying this now? And will it surprise anyone that the Labour leader of Glasgow opposes SNP Government legislation?"
A Scottish Government spokeswoman said: "An independent evaluation of this legislation is currently being undertaken by researchers at the University of Stirling.
"This process will provide us with a comprehensive, quality assured and evidence based evaluation report on the legislation."