Summonses for unlawful possession of marijuana, a noncriminal violation, can come with fines up to $100, though city officials said the fine amounts were ultimately up to judges and could change depending on someone’s criminal history.

Defense lawyers say the real impetus for marijuana enforcement is often not an arrest or summons itself, but rather the opportunity for police officers to stop and search people and check for open warrants in other cases. They said the fact that the new policy preserves officers’ authority to search people they stop for smoking marijuana suggests that the Police Department believes smokers merit closer scrutiny than people, for example, who are caught drinking in public — something they say there is little evidence to support.

Beyond the arrests based on someone’s criminal history, people caught smoking in public would also be arrested if they did not have identification or were smoking in a way that created an “immediate threat to public safety,” said Rodney Harrison, the Police Department’s chief of patrol. He said, for example, that officers would be given discretion to arrest people who are smoking around children in a park or smoking while operating heavy machinery. To protect against unsafe driving, people caught smoking in the driver’s seat of a car would also be arrested.

Chief Harrison said that officers could make a case for arresting someone in a place that has been the subject of repeated public complaints about marijuana smoke. He said every arrest has to be approved by a precinct supervisor.

He said the police had to arrest people caught smoking while on parole or probation because it represented a violation of the terms of their release. The number of people held in city jails on state parole violations has increased in recent years, a trend that runs counter to the city’s goal of closing Rikers Island.

The district attorneys in Manhattan and Brooklyn both said recently that they planned to stop prosecuting many marijuana cases, creating the potential for a patchwork of different policies across the city’s five boroughs. The city’s new policy was intended to create a more consistent strategy. And the Brooklyn district attorney, Eric Gonzalez, who appeared alongside the mayor at Tuesday’s news conference, voiced support for the exceptions in the city’s new policy.

But the Manhattan district attorney, Mr. Vance, said in an interview that while the new policy was a step forward, continuing to arrest people on the basis of their criminal records “stands in contrast with the overarching goal of increasing fairness at the same time as maintaining public safety.”