ALBANY — The New York Police Department, the mayor and the city’s top prosecutors on Monday endorsed a proposal to decriminalize the open possession of small amounts of marijuana, giving an unexpected lift to an effort by Gov. Andrew M. Cuomo to cut down on the number of people arrested as a result of police stops. 

Mayor Michael R. Bloomberg, whose Police Department made about 50,000 arrests last year for low-level marijuana possession, said the governor’s proposal “strikes the right balance” in part because it would still allow the police to arrest people who smoke marijuana in public.

The marijuana arrests are a byproduct of the Police Department’s increasingly controversial stop-and-frisk practice. Mr. Bloomberg and police officials say the practice has made the city safer, but, because most of those stopped are black or Hispanic, the practice has been criticized as racially biased by advocates for minority communities.