Short of an act by the Legislature, the directive ordered by Mr. Paterson is the one of the strongest statements a state can make in favor of gay unions.

“Basically we’ve done everything we can do on marriage legislatively at this point,” said Sean Patrick Maloney, a senior adviser to Mr. Paterson. “But there are tools in our tool kit on the executive side, and this is one.”

The directive cited a Feb. 1 ruling by a State Appellate Court in Rochester that Patricia Martinez, who works at Monroe Community College and who married her partner in Canada, could not be denied health benefits by the college because of New York’s longstanding policy of recognizing marriages performed elsewhere, even if they are not explicitly allowed under New York law. The appeals court said that New York must recognize marriages performed in other states that allow the practice and in countries that permit it, like Canada and Spain.

Monroe County filed an appeal with the state’s highest court, the Court of Appeals, but it was rejected on technical grounds. The county has not decided whether to file another appeal, a county spokesman said on Wednesday. The Court of Appeals has previously ruled that the state’s Constitution did not compel the recognition of same-sex marriages and that it was up to the Legislature to decide whether do so.

Groups that oppose gay marriage said the governor was essentially trying to circumvent the Legislature.

“It’s a perfect example of a governor overstepping his authority and sidestepping the democratic process,” said Brian Raum, senior legal counsel for the Alliance Defense Fund, a national organization opposed to same-sex marriage. “It’s an issue of public policy that should be decided by the voters.”

Gay rights advocates, however, applauded Mr. Paterson, saying the broad directive would make it clear that gay couples wed in other states were entitled to all of the benefits of marriage in New York and relieve them of the burden of challenging or suing individual agencies.