The move has been backed by Edinburgh Secular Society.
At present, education authorities are required to provide religious education as well as opportunities for religious observance.
But mother-of-one Veronica Wikman wants things such as hymn singing and worship at assemblies scrapped.
Under the Education (Scotland) Act 1980, schools have a statutory requirement to offer religious education and religious observance. This legislation originally dates from 1872.
Scottish government guidelines state every school should provide opportunities for religious observance at least six times in a school year.
Ms Wikman has set up a petition on the Edinburgh City Council website calling for a local vote on a proposal to discontinue religious observance in non-denominational schools in the city.
She said: "Religious observance has nothing to do with education but everything to do with religious indoctrination.