The Campaign for Muslim Schools - an alliance of all Glasgow's main mosques and Muslim organisations - has targeted two primary schools in Glasgow.
The campaign claims that the denominational St Albert's Primary in Pollokshields on the south side of the city (where more than 80 per cent of pupils are Muslim) is making children take part in Christian rituals such as the Lord's Prayer and mass.
Osama Saeed, co-ordinator of the campaign, claimed the school had refused to let children opt out, despite complaints from parents.
"The problem for the church is that, if it allowed children not to take part in these rituals, the school would effectively cease to practise Catholicism," he said. "This does not seem a sound way to justify the existence of a faith school, though.
"Clearly, the parents of that area find a faith school, even if it is of another denomination, preferable to a secular one. But surely it should be possible for them to have one that is relevant to their own faith."
The campaign has also called for Willowbank Primary in the Hillhead area to be saved from closure by converting it into a Muslim school. A decision is expected from Glasgow City Council in February.
A council spokeswoman denied that Muslim pupils were being forced to take part in Christian ceremonies.
"The pupils at St Albert's Primary, a Roman Catholic school, attend through parental choice. Any parent can request that their child does not take part in religious observance.
"Glasgow City Council is not opposed to Muslim schools in principle, but we do not have any plans to establish such a school. There is no clear evidence of a consensus in favour of such a major development, from within the diverse Muslim community itself or from the wider community."
The spokeswoman added that the issues could not be addressed on an individual school basis.
Michael McGrath, director of the Scottish Catholic Education service, said St Albert's was often used as "a symbolic flag to wave" to make the case for a Muslim school. It was, however, for the Muslim community to make that case and it should not become an issue between the Muslim community and Catholic Church.
In principle, the Catholic Church supported the case for other denominational schools in Scotland, Mr McGrath said, so long as a case could be made.
He added that the values promoted at St Albert's were very much Catholic ones, but that the significant majority of Muslim pupils would affect how the school interpreted other faiths and understood other festivals.