A Christian bakery owner who refused to make a cake with a slogan supporting gay marriage says he's been threatened with legal action.

Ashers, based in Northern Ireland, declined the order earlier this year, with the Equality Commission then taking on the case on behalf of the customer.

The bakery manager says he's now received a letter claiming he's breached legislation and he'll face legal moves if compensation isn't offered.

Daniel McArthur, general manager of the 22-year-old company, said he and the directors considered the cake design and decided the order was "at odds with our beliefs" and "in contradiction with what the Bible teaches".

"Marriage in Northern Ireland has not been re-defined. It still is defined as being a union between one man and one woman" he said in an online statement.

The Newtonabbey bakery, which is one of six run by the McArthur family - employing 62 people - refunded the customer in full and thought that was the end of the matter.

The Christian Institute, which is providing the bakery with legal support, said the request for the cake was made in May by a "volunteer LGBT activist".