Scotland - Members of the Faith in Marriage group include, among others, the United Reformed Church, the Quakers, Buddhists and the Pagan Federation.
Same-sex couples can enter into civil partnerships, but can not have a marriage ceremony in church.
Larger religious organisations such as the Church of Scotland and the Roman Catholic Church are against change.
The Scottish government, which held a 14-week consultation into the matter, said it "tends towards the view" that same-sex marriages should be introduced.
The Faith in Marriage coalition said not allowing marriage in church and was discriminatory and "an unacceptable infringement by the state on our freedom of religion and belief".
In its joint letter the coalition warned that it would "strongly oppose" attempts to restrict same-sex marriage to civil-only ceremonies.
Instead, it is seeking assurances from MSPs that any proposed legislation would "protect and extend" freedom of religion and belief by "giving those religious and humanist bodies that do want to conduct same-sex marriage the right to do so".
The coalition's letter reads: "We respect the religious freedom of those bodies that currently do not wish to conduct same-sex marriages, and we agree that there should be a mechanism in place to ensure that they do not have to. This is a position widely supported by equal marriage campaigners.
"We do, however, note with dismay that little mention has been made by politicians or the media of the rights of those religious and humanist bodies that do wish to conduct same-sex marriages.
"We are concerned that this debate is being framed by some as 'LGBT people vs religion', when in reality there are many LGBT people of faith and there is a great divergence of opinion on same-sex marriage amongst - and within - religious bodies."
In a separate move, campaign group Scotland for Marriage - which is against changing the law - said it hoped to leaflet every house in Glasgow ahead of Thursday's council election, at a cost of £15,000.
The group, which is backed by organisations including the Catholic Bishops' Conference of Scotland, the Christian Institute, the Evangelical Alliance and Destiny Churches, said it also planned to use mobile advertising vans to put across its opposition to same-sex weddings.
In January, political leaders signed a pledge to support a campaign to legalise gay marriage.
Leaders of the Labour, Liberal Democrat, Green and Conservative parties signed up at an event at Holyrood which was marked with a specially-created "equal marriage" cake.
The Scottish government is currently considering the responses it received to a public consultation on the issue, and has said faith groups and their celebrants should not be obliged to solemnise the ceremonies.