The case disputes the decision of Ashers Bakery to turn down an order for a cake with an image of Sesame Street puppets Bert and Ernie below the motto Support Gay Marriage.
According to the Belfast Telegraph, Judge Brownlie said: “It is not a straightforward area of the law.
“Obviously this is a case in which I propose to reserve my judgement.”
The Equality Commission, which champions complaints of those who claim to have been discriminated against on the grounds of their religion, race, age, gender or sexuality, is seeking damages against Ashers.
It said that if the bakery was allowed to refuse to do business with a minority group, a precedent would be set for discrimination.
Christian charity the Christian Institute is backing Ashers in the case, which it said proved the need for the law to reasonably accommodate family-run businesses with firmly held beliefs.
The cake, ordered to celebrate International Day against Homophobia and Transphobia on17 May 2014, was supplied by another bakery.