Much of the attention has been focused on Staten Island, but the Bronx has been hardest hit in the crisis: four of the top five city neighborhoods ravaged by overdose deaths were in the borough, according to the city; the fifth was the southern part of Staten Island. The Bronx has the highest fatal overdose rate in the city, which nearly doubled in 2015, the most recent year for which detailed data is available. The borough saw the biggest increase in the city, followed by Queens, Staten Island and Brooklyn.

Mr. de Blasio took pains to stress the newness of the plan, while at the same time disputing the notion that his administration had come late to the issue. But he acknowledged that the steep rise in opioid overdose deaths in 2016 — up roughly 50 percent in one year — provided a “wake up call.”

“The last year has been very sobering,” he said.

City officials estimate there are about 85,000 heroin users in the city, a number they say is likely low given the private nature of drug abuse. Four out of five people who use heroin started using prescription drugs, the officials said, a scenario Mr. de Blasio tied to the “corporate greed” of pharmaceutical companies that make and sell opioid pain medications.

Around Lincoln Hospital, a predominantly black and Latino neighborhood, long lines extend from the methadone clinics that dot a landscape where public housing towers look over small apartment buildings, clothing stores, fast-food chains and family restaurants. Children walking to and from school often pass zoned-out drug addicts, and hypodermic needles litter some side streets. The neighborhood, combined with Hunts Point, has the highest the rate of fatal overdoses in the city.

In the plan, the largest portion of spending goes to providing naloxone, with $10.3 million to be spent in the 2019 fiscal year. About $3 million will go to expanding access to buprenorphine, a drug that can help suppress symptoms of withdrawal and decrease cravings, and methadone.

The police were responsible for a small portion of the naloxone “saves” by city first responders, with 51 last year. By contrast, emergency medical technicians and firefighters gave the drug to 2,067 patients over the same period, according to the Fire Department.

“Making naloxone as widely available as possible in the midst of an opioid overdose crisis is a no-brainer, but it’s only going to go so far,” said Dr. Andrew Kolodny, who directs opioid policy research at Brandeis University’s Heller School for Social Policy and Management.