By Chris Michaud

NEW YORK (Reuters) - Supporters and opponents of gay marriage made 11th-hour appeals on Sunday as state lawmakers weighed a vote on making New York the sixth state – and the most populous -- to legalize same-sex marriage.

The measure that would make gay marriage legal, introduced by Governor Andrew Cuomo, a Democrat and strong advocate, is currently one vote shy of passage in the state Senate.

The state Assembly approved the bill by a wide margin last week, and Monday is the last day of the legislative session before summer recess.

New York's Archbishop, Timothy Dolan, reiterated his and the Catholic Church's opposition to gay marriage on Sunday, vowing to oppose "any radical bill to redefine the very essence of marriage."

"One has to wonder why the proponents of this radical redefinition, who claim overwhelming popular support, would not consider" a referendum "on such a drastic departure from traditional values?" he wrote on his blog.

Recent polls show statewide support for gay marriage.

Dolan wrote that the "government presumes to redefine" such sacred words as father, mother, husband and wife "at the peril of the common good."

In Albany, Senate Majority Leader Republican Dean Skelos has said the bill as written has prompted concerns over its religious clauses and exemptions.

The bill does not compel any member of the clergy to conduct same-sex marriages, but some Republican lawmakers are concerned the legal protection is not strong enough.

Skelos said Cuomo has indicated he was open to including more specific exemptions for religious groups.

The governor has lobbied for passage and said he remains cautiously optimistic the bill will come to a vote and pass.

Meanwhile gay marriage advocates, including Latinos United for Marriage Equality, rallied on Sunday.

"Our demand today is simple and reasonable: bring Marriage Equality to a vote on Monday," said Jake Goodman of the group Queer Rising, in a statement.

The group held a "Last Day of Marriage Inequality" rally in Manhattan's Union Square, where supporters carried signs that read "'I do'" support marriage equality" and "Be a leader: introduce the bill."

New Yorkers United for Marriage also held rallies around the state.

The stakes are especially high because New York would become the most populous U.S. state to allow gay marriage approved by lawmakers, spelling a huge gay rights victory.

The state-by-state battle over gay marriage has become a contentious U.S. social issue ahead of the 2012 presidential and congressional elections.

Five states -- Massachusetts, Connecticut, Iowa, New Hampshire and Vermont -- and the District of Columbia allow gay marriage, while four states have civil unions. Gay marriage is specifically banned in 39 states.

(Reporting by Chris Michaud; editing by Ellen Wulfhorst)