Almost three-quarters of people in the UK believe gay couples should be able to marry in Northern Ireland, a survey showed.
It is the only part of the country where same-sex marriage is illegal.
Supporters of change want Westminster to legislate in the absence of devolved powersharing at Stormont.
Northern Ireland's largest party, the Democratic Unionists, believe marriage is between a man and a woman and argue civil partnerships are available to same-sex couples.
Gay rights activist John O'Doherty said: "Justice delayed is justice denied.
"It is unacceptable and unsustainable to have a patchwork of marriage laws across these islands.
"The ongoing denial of marriage equality to people in Northern Ireland is an embarrassing stain on the UK's LGBT rights record and cannot be allowed to continue."
According to YouGov polling for PinkNews, 70% of people in the UK agreed that same-sex marriage should be allowed in Northern Ireland, up from 65% last year.
Total sample size was 1,720 adults and covered the whole of the UK including Northern Ireland.
A total of 55% of those living there agreed.
The polling reflected cross-party support, with Tory voter backing rising from 54% to 62% compared with a similar study last year.
The PinkNews publication focuses on LGBT issues and is hosting a reception at Stormont for political leaders this week.
A DUP speaker is not scheduled to attend.
Democratic Unionist leader Arlene Foster was present at a similar event last year.
Same-sex marriage is one of the issues in contention between the DUP and Sinn Fein as they attempt to restore powersharing during this summer's negotiations.
During a vote in November 2015, Northern Ireland's Stormont Assembly members supported same-sex marriage by a majority of 53 votes to 52.
The motion was blocked by the DUP using a veto measure known as a petition of concern.
Mr O'Doherty from the Rainbow project LGBT support organisation said: "We are seeking the support of parliamentarians and people from across these islands to compel the British Government to implement marriage equality across the whole of the UK without delay."
PinkNews chief executive Benjamin Cohen said it was clear that, across the country, there was strong support for same-sex marriage to be legalised in Northern Ireland.
"Today, the UK is the only country where marriage means a different thing depending on where you live, and it is incumbent on all politicians to work together to ensure that everyone, LGBT+ or straight has an equal stake in our society."