The Christian Institute has condemned a motion by Ben Bradshaw MP "to enable clergy of the Church of England to conduct same sex marriages on Church of England premises in certain circumstances".
The organisation has called the Labour MP's motion a "brazen attack on religious liberty".
The Christian Institute is calling on MPs to reject the motion when it is expected to come up for debate in Parliament next week.
Protections in the Marriage (Same Sex Couples) Act 2013 means that at present, churches cannot be compelled to conduct same-sex wedding ceremonies.
The Bill proposing to undo those protections is being introduced under the Ten Minute Rule, and has the support of Dame Margaret Beckett, Harriet Harman and Sir Peter Bottomley.
Few Ten Minute Rule Bills become law but are used to draw attention to certain issues and test the opinion of the House.
Mr Bradshaw said he hoped his motion would be "a precursor to actual legislation".
A spokesperson for the Church of England has told The Times that members of the Church of England's parliament, the General Synod, will "no doubt listen carefully to views expressed in Parliament".
The Christian Institute's Director Colin Hart said that the motion "flagrantly interferes with Church doctrine and must be decisively rejected".
"If successful, this brazen attack on religious liberty undermines, and could ultimately wreck, the whole package of protections for churches."
Anglican theologian Dr Ian Paul raised similar concerns in comments to The Times: "Just think which countries in the world allow the secular state to dictate religious belief. It's not a pretty list."
