Fiji's Media Industry Development Authority says media organisations should not publish or broadcast material in a form likely to promote discord, but are free to report matters of national interest.
The Authority's chairperson, Ashwin Raj, made the comment after last week's report in the Fiji Sun which quoted the prime minister as saying if a women wants to marry another woman, they should do so in Iceland and stay there.
Mr Raj says media organisations have to be sensitive to and particularly careful about the possible effects of discriminatory references to vulnerable minorities in prejudicial or pejorative contexts.
He goes on to say that Fiji needs to have a deep and meaningful discussion on the issue that goes beyond what he calls the cul de sac of marriage.
A human rights advocate, Shamima Ali, has described the prime minister's comments as disheartening.