By NICHOLAS CONFESSORE and MICHAEL BARBARO

Updated, 3:45 p.m. | ALBANY — Three wavering Democratic lawmakers in the State Senate on Monday announced that they now support the legalization of same-sex marriage in New York, marking a potential turning point for the long-debated measure.

Within an hour of the announcement by the three Democrats, a Republican senator said that he, too, is open to supporting same-sex marriage.

“If the bill comes to the floor the way that I would like to see it, I will support it,” Senator James S. Alesi, a Monroe County Republican, said before going into a meeting with Gov. Andrew M. Cuomo. Mr. Alesi did not elaborate.

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