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.

Most of the candidates in the Democratic mayoral primary have taken more centrist positions on policing. Crime has fallen in the city in recent years after a pandemic spike, yet felony assaults remain high and many New Yorkers worry about violence on the subway.

Former Gov. Andrew M. Cuomo, who leads in mayoral polls, has argued that the city is in crisis and said he would hire 5,000 more police officers. He has criticized candidates who supported the “defund the police” movement, including Mr. Mamdani, who called for reducing the police budget when he was an Assembly candidate in 2020.

Brad Lander, the left-leaning city comptroller, has said he would keep the current police commissioner, Jessica Tisch, and hire hundreds of police officers. Zellnor Myrie, a state senator who was once pepper sprayed by the police, wants to hire 3,000 officers.

The Police Department is facing a staffing crisis as officers quit and it struggles to replace them. It has about 34,100 officers, down from a peak of 40,000 in 2000, according to department figures and the city’s Independent Budget Office.

Civil rights groups and progressive elected officials have long called for a more expansive view of public safety that goes beyond policing and focuses on reducing poverty and addressing mental health problems. They have criticized stop-and-frisk policing and supported the use of violence interrupters, who try to defuse disputes before they escalate.

Mr. Mamdani, who has risen to second place in the polls, has been a strong fund-raiser and has released popular plans for free buses and city-owned grocery stores.

He, too, said he would consider keeping Ms. Tisch as police commissioner and praised some of her policies, including addressing concerns about corruption and reducing the size of the department’s communications staff.

His proposed Department of Community Safety would have a budget of roughly $1 billion, comprising $600 million for existing programs and $450 million in new funding. It would be run by a commissioner-level position, and Mr. Mamdani would eliminate the deputy mayor for public safety, a role that Mayor Eric Adams revived in 2022.

He would expand programs like the Behavioral Health Emergency Assistance Response Division, or B-Heard, which sends teams of mental health professionals, rather than the police, to certain emergencies. He also wants to deploy “mental health navigators” in neighborhoods and outreach teams at 100 subway stations to connect people with services.

Mr. Mamdani said that he would pay for the additional costs related to the new agency — and for his broader affordability proposals — by raising taxes on wealthy residents and large corporations and through a better use of existing city funds and stronger enforcement of tax policy.

It seems clear that Mr. Cuomo intends to attack his left-leaning rivals for favoring progressive approaches over what he considers more pragmatic solutions, especially concerning public safety.

When Mr. Mamdani, Mr. Lander, Mr. Myrie and a fourth candidate, the City Council speaker, Adrienne Adams, were backed by the left-leaning Working Families Party on Saturday as part of the group’s initial endorsement, Mr. Cuomo’s team had a quick response.

Rich Azzopardi, a spokesman for the Cuomo campaign, called the four Democrats a “fringe group of extremists who brought us anti-Israel, ‘defund the police’ and other failed policies that have brought our city to the brink.”

Mr. Adams, a former police officer, successfully campaigned in 2021 on a vow to improve public safety. He brought back contentious police units that focus on removing guns from the streets but have also contributed to a rise in illegal police stops.

Mr. Mamdani said that Mr. Adams had promised as a candidate to bring down crime and to reform the Police Department, but then “betrayed” voters by focusing only on the first issue.

“Democratic primary voters prefer a comprehensive approach with fully funded treatment programs and gun violence prevention and a focus on outcomes,” he said.

Alana Sivin, a director at the Vera Institute of Justice, a criminal justice nonprofit, said that Mr. Mamdani’s plan embraced the “full range of tools” that are needed to improve public safety and “successful precedent in other parts of the country,” including the Community Safety Department in Albuquerque, N.M., which has responded to more than 82,000 calls for service.

Maria Cramer contributed reporting.