Even as same-sex marriage has become a popular cause for elected officials and celebrities in New York, Mr. Bloomberg has emerged as a particularly important advocate given his visibility, wealth and longtime support for conservative politicians. Last week he went to Albany to lobby Republican senators, and on Wednesday he hosted a star-studded fund-raiser for gay rights advocates at the Upper East Side headquarters of his foundation.

In his speech on Thursday, Mr. Bloomberg reiterated his call for the State Legislature to vote on same-sex marriage before the legislative session ends in June, arguing that New Yorkers “deserve to know where our elected officials stand on this historic issue.” That stance has put him at odds with Gov. Andrew M. Cuomo, a Democrat who also supports same-sex marriage, but who has said he would not seek a vote unless he is confident that the measure would pass.

The State Assembly, controlled by Democrats, has endorsed same-sex marriage several times in the past, but the State Senate, controlled by Republicans, has not. So far, advocates appear no closer to prevailing this year than the last time the Senate took up the issue, in late 2009.

The tone of the speech was unusually personal for a mayor known for dispassionate number-crunching and policy analysis. Mr. Bloomberg was introduced by a niece, Rachel Tiven, who is gay. At one point, he said that he had grown tired of trying to explain to gay friends, relatives and staff members why the government was denying them the right to wed.