In New York, playing to voters’ concerns about crime has become a popular strategy, successful enough that even left-leaning Democrats have embraced calls for more police officers.

Zohran Mamdani, a democratic socialist rising in the polls in the New York City mayor’s race, has chosen a different approach.

His 18-page public safety plan, which will be released on Tuesday, does not call for hiring more police officers, as several of his rivals have done. Mr. Mamdani, a state assemblyman from Queens, would instead create a city agency called the Department of Community Safety that would focus on expanding violence interrupter programs and mental health teams that respond to 911 calls.

“The police have a critical role to play,” he said in an interview. “Right now, we’re relying on them to deal with the failures of our social safety net. This department will pioneer evidence-proven approaches that have been successful elsewhere in the country.”

Mr. Mamdani said he also would eliminate the Police Department’s huge overtime budget and a unit known as the Strategic Response Group that responds to protests.

His criminal justice platform is likely to appeal to his supporters on the left. But some voters appear to be tilting away from progressive theories on reducing crime. The city moved to the right in the presidential election in November after President Trump portrayed the city as crime-ridden and raised concerns about violence by immigrants.