It follows a decision on Monday by the Stormont Assembly to reject the introduction of gay marriage for a fourth time.
A total of 96 MLAs took part in the vote and 49 voted against the Sinn Féin motion calling for civil marriage equality for all, with 47 in favour.
Sinn Féin, SDLP and five Alliance MLAs supported the motion. The DUP opposed it and the Ulster Unionists were given a free vote on the issue.
Alliance Party Deputy Leader Naomi Long, a Christian, said she would like to see more debate on the issue before she would consider fully supporting a referendum: "I think what we need to have at this stage in Northern Ireland is more respectful engagement between faith communities, between the LGBT community and between the wider community about how we can ensure that everyone's rights and freedoms are properly protected, I don't believe we have the balance right in Northern Ireland at this time," she told Premier's News Hour.
"Part of the fear I believe in Northern Ireland, I think it is an unjustified fear, but it is a real fear that people have; is that if we have same-sex civil marriage provided that it will in some way prevent those of faith having a view on homosexuality or expressing a Bible based view that in contrary to that," added Ms Long.
Northern Ireland is the only part of the UK that has not introduced equal marriage for gay couples.
Alliance Party Deputy Leader Naomi Long speaking to Premier's Des Busteed:
