The bill was drawn up by the Democratic Unionist Party member, Paul Givan, after a Christian-run bakery faced legal action for refusing to bake a cake with a pro-gay marriage slogan.
The clause would allow businesses to refuse to provide some services if they clash with their religious convictions.
A Catholic delegation said that any change to the law would have to be carefully defined, to prevent it from leading to spurious claims of religious conscience.
Catholic leaders including the Bishop of Down and Connor Noel Treanor said politicians must accept there was a real problem that needs to be addressed.
He said it would be wrong to swap one form of discrimination for another.
The Catholic Church has concerns about the impact of anti-discrimination law on its adoption agency and, potentially, its marriage guidance service.
Mr Givan is currently carrying out a consultation into a Private Member’s Bill, but opponents have pledged to block the conscience clause bill and say it would legalise discrimination.
Mr Givan said that “Christians do not feel there is space being made for their religious beliefs”.
“The issue at stake is when you’re asked to produce a particular service,” he said.
“It’s about the message you’re being asked to endorse, not the messenger who’s asking for it. Say someone comes in and asks for a cake saying ‘I support gay marriage’ – that’s a direct form of communication you’re asking this Christian-owned company to produce and they don’t want to be forced to do that.
“I don’t think that’s unreasonable, I think that’s tolerant and if we live in a pluralist, liberal society we need to make space for difference.”
Mr Givan’s bill aims to create a legal exemption on grounds of strongly held religious beliefs.
Last month, more than 1,000 people gathered at Belfast’s City Hall to protest against the bill.