A parent in Edinburgh has launched a petition calling on the city council to look at banning religious observance in non-denominational schools.
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.
"The Church of Scotland has not owned our schools since 1872. It should retain no privileged access to the education of my child or any other."
Edinburgh Secular Society has warned that religious observance creates an "open door for external religious groups to target children and instil their religious beliefs".
Neil Barber from the society said: "Religious education is a balanced, important part of education if taught in a comparative and philosophic way.
"Religious observance, on the other hand, is imposed as truth, sometimes by evangelising visitors."
Parents do have a right to withdraw their children from religious lessons and assemblies.
Speaking on BBC Radio Scotland's Call Kaye programme, Reverend Ian Galloway, from Gorbals Parish Church in Glasgow, said: "Religious observance in schools is not about the church, or anybody else, having free access to children to do what they like.
"Religious observance is not about direct indoctrination of religion and I would be absolutely against any form of indoctrination in any school.
"We are concerned with advancing the experience of young people, helping them to grow up as full, healthy human beings and that includes being able to explore the spiritual dimension of their lives, along with the others."
Ms Wikman's petition will be active until 7 May. If it achieves 500 or more signatures it will be heard by the council's Petitions Committee.
A City of Edinburgh Council spokeswoman said: "It would be inappropriate for us to comment on a live petition.
"The whole purpose of the Petitions Committee is to give the people of Edinburgh a chance to raise issues of public concern and in turn give councillors the opportunity to consider the need for changes.
"If this petition receives the amount of signatures required it will be considered at a future Petitions Committee."