The government has so far vetoed every attempt to secure equal marriage and has said it would veto this new attempt too, considering that civil unions are sufficient for same-sex couples.
According to Premier, a number of Northern Ireland Assembly members are attempting to by-pass the administration by pursuing new legislation through Private Members' Bills.
"I am in favour of marriage equality - that is why in this mandate I am determined to make what progress I can to put marriage equality on the statute book," Finance Minister Mairtin O Muilleoir said.
"I would like to proceed by way of an Executive Bill and I will at the earliest opportunity seek Executive agreement to consult on the issue."
If a legislation was to be introduced it would allow religious institutions not to celebrate same-sex marriage if they so wish.