The warnings had been dire: A law broadening the types of lawsuits that can be filed over accusations of police profiling would make New York City less safe. It would cut into terrorism investigations and anti-gang initiatives and make police officers wary of stopping suspects on the street.

But in roll-call rooms around the city over the weekend, every officer in the New York Police Department received a more sober summary of the law, which passed despite Mayor Michael R. Bloomberg’s veto in August and took effect on Wednesday.

The four-page message, sent to all commands on Friday and read to officers before their shifts over the last few days, sought to clarify the law and explain how race, as well as other demographic features, can be considered by an officer in deciding whether to act. While race can be a factor, it cannot be the only factor. For example, if a victim “describes a crime suspect by race, sex, clothing description and direction of travel, a person who has those physical characteristics and is traveling in the direction described may be the subject of law enforcement action,” the internal memo reads.

“It would be unlawful,” it adds, “to stop or otherwise engage that individual if the deciding factor for doing so was that he/she matched only the race of the person described in the radio run.”