A firm commitment to deliver same-sex marriage must be made before the next Executive in Northern Ireland is formed, campaigners said.
A significant majority of the Assembly elected last week support the change, the country's main LGBT organisation said.
The Democratic Unionists do not have enough seats to mount a veto but other unionists could join a pact to block the measure.
The Love Equality coalition said it would be a litmus test of any new government in Northern Ireland.
Declan Meehan said: "All of the people of Northern Ireland must be served by the incoming government - that includes the LGBT community.
"Before any new Executive is formed, there must be a firm commitment to deliver equal marriage legislation.
"Without that, we know it will be another five years of LGBT people being treated as second-class citizens of Northern Ireland."
He represents Cara-Friend, one of Northern Ireland's main LGBT community organisations which provides counselling and befriending.
In 2015, a majority of Northern Ireland Assembly members voted for same-sex marriage for the first time.
But the motion was blocked after the DUP deployed a petition of concern that required the proposal to achieve a cross-community majority.
Following last week's poll, the DUP won 28 seats - two short of the 30 needed to pass a petition of concern by themselves.
However, unionists from the Ulster Unionist Party and Traditional Unionist Voice, who believe marriage is solely between a man and a woman, could support the DUP on the issue.
Clare Moore of the Irish Congress of Trade Unions (NIC-ICTU), the representative body for 34 trade unions with over 215,000 members across Northern Ireland, said: "Any new Executive must be willing to be a government for all the people of Northern Ireland.
"A key litmus test of this is whether it is willing to pass equal marriage legislation, as supported by an overwhelming majority of people and now also of Assembly members.
"The Love Equality campaign knows that a very significant majority of members of the new Assembly support equal marriage. The will of the people must be respected.
"That means there must be no more delay in delivering marriage equality."