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.

The three Democratic senators -- Joseph P. Addabbo Jr. and Shirley L. Huntley of Queens and Carl Kruger of Brooklyn -- all voted against the measure in 2009, when it failed by a wide margin. Their switch to the yes column leaves all but one Senate Democrat supporting same-sex marriage -- and the fate of the legislation in the hands of the Republican majority in the chamber.