Taoiseach Enda Kenny has been called on to declare his support for marriage for lesbian and gay couples.
The Gay and Lesbian Equality Network (Glen) said it was time for Mr Kenny to follow Justice Minister Alan Shatter and Tanaiste Eamon Gilmore who have both publicly supported it.
Glen chair, Kieran Rose, said the forthcoming Constitutional Convention provides the opportunity to address all the issues.
"The Taoiseach, in declaring his support for civil marriage, would give clear political leadership, building on the success of civil partnership and the very strong public support for progress to the next step," he said.
Earlier Mr Shatter indicated his support for gay marriage.
"I believe that individuals should be allowed to get on with their lives freely in circumstances in which their circumstances don't detrimentally impact on others," he said.
"I fully support equality, I fully support civil partnership - and I think it's in the public interest this Constitution issue be addressed in the Constitutional Convention that is going to be held."
On Sunday, Mr Gilmore said he believed in gay marriage, adding that the right of gay couples to marry was a civil rights issue for this generation.
Mr Shatter said there was nothing the Tanaiste said which he personally disagreed with.
However, he admitted the difficulty is in Ireland's Constitution which, under Article 41, makes reference to marriage.