Thousands of people have taken part in rallies for marriage equality in both Belfast City Centre and Derry.
Campaigners say they organised Saturday's simultaneous events to protest against the ongoing failure to introduce marriage equality here.
Northern Ireland is the only part of the United Kingdom which does not have legislation for couples of the same-sex to marry. The Republic of Ireland made history when marriage equality was brought about by a referendum in May 2015.
On Saturday campaigners insisted any deal to restore power-sharing at Stormont must include reform of a controversial voting mechanism that has blocked a law change here.
A majority of MLAs backed the introduction of same-sex marriage the last time it was debated in the Assembly before the institutions collapsed at the beginning of last year, but the use of the petition of concern by the DUP rendered that irrelevant.
The party has said it is willing to scrap the petition entirely if others, including Sinn Fein, agree.
On Saturday John O'Doherty, a prominent activist with the Love Equality coalition said: "No party or group of MLAs should hold a veto over people lives, over people's rights.”
At the rally in Belfast Armagh-born Labour MP Conor McGinn, who failed in a recent bid to change the law through a private member's bill at Westminster earlier this year, warned Mrs May the issue was "not going away".
Mr McGinn MP said: "The message from the thousands here today in Belfast is loud and clear. It is a message for the Prime Minister and the Government, and it is: we love equality, we stand with LGBT couples, we demand the same rights as everyone else in the UK and the island of Ireland, and we want equal marriage now.”
While there is a resistance from some on the prospect of a change to the legislation here, politicians are under growing pressure as the issue continues to be a hot topic of debate.