Nevertheless, he has said he is committed to putting the measure to a vote in Albany sooner rather than later.

“The timing was always right,” Mr. Paterson said on Tuesday as he announced an economic-development grant in Nassau County. “It’s just who is willing to take that step. And I am.”

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Once Mr. Paterson introduces the bill, a step that he is expected to formally announce on Thursday morning, the focus will shift to the Assembly, where the measure passed in 2007 by a vote of 85 to 61, and is expected to pass again this year.

“And I think that all could happen rather quickly,” said Micah Z. Kellner, a Democratic assemblyman who represents the Upper East Side. Once the Assembly acts, it will be up to Senate Democrats, who control the chamber 32 to 30, to decide whether to bring it to the floor for a vote. Some in the Senate, including its only openly gay member, Thomas K. Duane, have said they want the bill to be voted on only if its passage is certain.

Some same-sex-marriage supporters said they hoped that by introducing the measure now, when it is likely to receive plenty of attention after the Iowa Supreme Court’s decision this month overturning a ban on same-sex marriage and the Vermont Legislature’s vote last week to override a veto of a bill allowing gay couples to marry, the governor would create momentum for the bill.

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“Maybe by coming out publicly like this and reaffirming his support for marriage equality, the governor can sway some colleagues in the other house who might be nervous about voting for this,” said Matthew Titone, a Democratic assemblyman from Staten Island. “I think it’s an opportunity for him to show people that he really believes in something.”

But cracking the Senate Republican conference, which is known for its unanimity and solidarity, will be a difficult task, same-sex-marriage supporters concede. Republican leaders have said they are not budging on the issue.

“Our conference hasn’t supported gay marriage, and nothing has changed,” said John McArdle, a spokesman for Senate Republicans.

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But Mr. Duane said that he had assurances from some Republicans that they would vote for the bill. He declined to name them.

Still, Mr. Duane said that while the governor’s bill was an important gesture, it could end up being ultimately just that.

“It’s still only paper, words, unless we all fight to make it a reality,” he said.