ALBANY, N.Y. — Gov. David Paterson on Monday urged lawmakers to legalize same-sex marriage in New York, calling it “an issue that touches on the very core of our citizenship.”

His request raises the hopes of gay advocates who suffered a major defeat in Maine when voters repealed that state’s same-sex marriage law last week.

In New York City, Christine Quinn, the openly gay council speaker, quickly weighed in by offering an impassioned plea for the state Senate to pass a bill legalizing same-sex marriage.

In a rare midyear address to a joint session of the Legislature, the Democratic governor singled out his gay marriage proposal in a lengthy agenda for Tuesday’s extraordinary session that will mostly be devoted to addressing the state’s $3.2 billion budget deficit.

“It is an issue that in many ways speaks to the very foundation of our democracy,” Paterson said of gay marriage. “I would like it addressed as immediately as possible, because justice delayed is justice denied. I am asking the members of the New York state Senate on both sides of the aisles to take up and pass the marriage equality legislation this week.”

It was the only time his 15-minute address was interrupted by applause, but it was only a smattering, with perhaps half the legislators refusing to clap.

However, in a signal that usually indicates progress in negotiations in Albany, Paterson changed his time frame for adoption from Tuesday, the only day so far he called the Legislature into extraordinary session, to sometime this week.

Then Paterson made a personal plea, following his framing of the issue a year ago as a civil right, and his recent promise to have the bill passed and signed into law by the end of the year.

The Rev. Jason McGuire of New Yorkers for Constitutional Freedoms said Tuesday’s results in Maine have shown even moderate Republicans that they can’t afford to back the measure going into the 2010 elections. He said the group is confident they have 35 or 36 senators opposed to the measure, which would block passage in the 62-seat house.

“God established marriage and I don’t think the state has a right to redefine it,” McGuire said. But he said the concern is really about children, who need to learn from mothers and fathers.

“Marriage is never about two people. It’s about future generations,” he said. “It does affect what’s good for society as a whole.”

Already passed in the Democrat-led Assembly, the measure wasn’t brought to the floor in the spring because there weren’t enough votes in the 32-30 Democratic majority to pass it. A few Democrats opposed the bill on religious grounds. Paterson changed that by putting the bill in his proclamation for Tuesday’s extraordinary session. However, Paterson can’t compel lawmakers to vote.

Now Republican leader Dean Skelos has released his members to vote as they see fit, without the usual bloc voting of the GOP.

“I think a lot of senators woke up this morning and realized a vote on marriage equality is real and could come tomorrow,” said Empire State Pride Agenda Executive Director Alan Van Capelle on Monday. “I believe, when this comes to the floor, these individuals will not be able to vote against their friends and their family.”

“Now is the time for them to stand up and be counted,” he said. “All eyes are on Albany.”

Meanwhile, the Democrat-led Senate continues to oppose Paterson’s deficit-fighting proposal, pitching its own plan that avoids painful cuts. The powerful health care lobby praised the ideas as innovative, but Paterson’s budget office called them gimmickry.

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AP Writer Valerie Bauman contributed to this report from Albany.