Mr. Cuomo, a Democrat, framed the issue as one of racial justice as well as common sense, saying that the police in New York City were wasting time, resources and good will making tens of thousands of unnecessary arrests. Possession of small amounts of marijuana is a crime only if the marijuana is in public view or if it is being smoked in public, but many of the marijuana possession arrests have been occurring when the police order someone stopped to empty his or her pockets, making the marijuana visible — a phenomenon the governor called an “aggravated complication” of the stop-and-frisk practice.

“It becomes a question of balance,” the governor said of the city’s police stops. “Part of the balance is the relationship with the community. I think the N.Y.P.D. and the mayor are making efforts to work with the community.”

The governor’s announcement was cheered by lawmakers from minority neighborhoods as well as by civil rights groups, who are increasingly looking to Albany and to Washington in an effort to rein in what they see as overly aggressive tactics on the part of the Bloomberg administration.

Black leaders also cited the governor’s proposal as a rare recognition of — and attempt to remedy — what they describe as a cultural and legal double standard: that young African-American men are being arrested in large numbers for an activity — using marijuana — that is prevalent, but with less frequent legal consequences, among whites of the same age.

“Some of our police officers are making race-based discretionary decisions on who they’re going to arrest for low-level marijuana possession,” said Leroy Gadsden, the president of a branch of the National Association for the Advancement of Colored People in Jamaica, Queens, and the chairman of the criminal justice committee for the statewide N.A.A.C.P. “Therefore, of course, if you’re a young, black male, even a female, you’re going to feel that you’re being targeted when you notice that your white counterparts are not being arrested for the same thing.”