Brad Lander, the New York City comptroller who is running for mayor, will unveil his signature campaign issue on Monday: trying to end homelessness on the streets and subways for people with severe mental illness.

The problem has vexed leaders in many large cities, but perhaps none more so than in New York, where a recent series of violent attacks on the subway has rekindled safety concerns and heightened calls for law enforcement and the courts to do more to keep troubled people off the streets.

Mr. Lander’s 75-page-plus plan calls for expanding subway outreach teams and embracing a “housing first” model that has been successful in other cities, including Houston and Denver. Mr. Lander would focus on roughly 2,000 homeless people with serious mental illness and place them in vacant apartments known as single-room-occupancy units, or S.R.O.s.

“New Yorkers are stressed out about lack of safety on the subway and our streets, and a huge amount of that is mentally ill homeless folks who, in some cases, become a real danger, as we’ve seen in recent weeks,” he said. “We dug in and realized this is a solvable problem.”

Mr. Lander said he believed he could get most or all homeless people with serious mental illness off the streets and into some form of supportive housing in his first two years as mayor. The plan would cost about $100 million in the first year, and roughly $30 million per year thereafter, with about half going toward renovating vacant single-occupancy apartments that would provide an array of on-site services.

The number of people living in the streets and subways of New York City was estimated at 4,140 last year — the highest level in nearly two decades. Rents have soared, and roughly one in eight public school students is homeless.

Those factors have helped make mental health and homelessness major issues in the mayoral race — with more attention focused on the problems after a woman was lit on fire and killed on a train, and subway riders have been pushed onto the tracks by people with mental illness.

Moving some of the city’s most fragile and least stable residents into permanent housing and having them stay requires a herculean level of coordination among multiple stakeholders. They include hospitals; jails; the criminal justice system; nonprofits that offer street medical services and provide housing; and city and state social service agencies and health authorities.

That has not stopped city leaders from trying to navigate that patchwork of bureaucracies.

Last week, during his fourth State of the City speech, Mayor Eric Adams announced a $650 million plan to address street homelessness that includes building new housing for people with serious mental illness and adding 900 “safe haven” beds, which are temporary housing options that offer more privacy and fewer restrictions than typical shelters.

Kayla Mamelak Altus, a spokeswoman for Mr. Adams, said in a statement that the mayor had “rejected the notion that leaving people to sleep on the street was acceptable” and helped move 8,000 New Yorkers from the subways into shelters, among other efforts. She said there was “still more work to be done,” pointing to the plan that the mayor just unveiled.

“It’s hard to imagine a fraction of this being achieved under Brad Lander, who would prefer to see our streets littered with encampments and our most vulnerable rotting away in filth,” she said.

Other mayoral candidates have pledged to address homelessness, including Jessica Ramos, a state senator from Queens who released a mental health plan last week. Ms. Ramos proposed building 20 community centers that offer therapy and filling vacant supportive housing units.

“As mayor, I will declare a mental health emergency on Day 1 of my administration so we can deliver services to suffering New Yorkers swiftly and effectively,” Ms. Ramos said.

Scott Stringer, a former comptroller, said in a statement that he would remove people who pose a danger to themselves or others and would expand mental health outreach teams. He said that New Yorkers felt “abandoned by city government.”

Zellnor Myrie, a state senator from Brooklyn, said the Adams administration was “letting too many people who are demonstrating behavioral disturbance fall through the cracks because of a byzantine network of programs and systems.” He said he would expand outreach teams and housing.

The issue has long bedeviled mayors. Bill de Blasio announced a $100 million plan to “end long-term street homelessness” in five years. After eight years as mayor, Mr. de Blasio acknowledged that the issue was his greatest disappointment.

Mr. Lander wants to rely on the “housing first” model that has allowed Houston to move more than 25,000 homeless people into apartments and houses. The approach moves the most vulnerable people straight from the streets into apartments, not into shelters, and does not require them to first wean themselves off drugs, complete a 12-step program or get a job. Evidence shows that the strategy keeps people housed, but it is unclear if it saves money or leads to better health outcomes.

New York City has about 40,000 supportive housing units, and most of their occupants moved there from shelters or other temporary housing. Mr. Adams’s administration started a “housing first” pilot program in 2022 that planned to reach 80 adults living on the street. Mr. Lander wants to significantly expand the program.

Mr. Lander’s plan would also create a centralized database for all mental health crisis responses to help prevent people from falling through the cracks.

Steven Banks, the city’s social services commissioner under Mr. de Blasio, said that Mr. Lander’s plan was “on the right track” based on his experience in city government and his decades at the Legal Aid Society, the main legal provider for poor New Yorkers.

The plan argues that Mr. Adams has failed to adequately address the city’s mental health crisis. It found that the mayor’s broad sweeps of homeless encampments had connected only three people with permanent housing during a period in 2022, and that his administration had not made enough progress on promises to create 360 therapeutic beds for people in jails and to create 15,000 units of supportive housing that include social services.

It also cited a lack of coordination among the various city agencies responsible for caring for those with mental health issues, including hospitals, outpatient treatment teams and homeless shelters — failures highlighted in a 2023 investigation by The New York Times.

Mr. Lander also seeks changes in the rules regarding involuntary hospitalization of people in psychiatric crisis, which are set by the state. Gov. Kathy Hochul said recently that she would push to loosen the standards for involuntary commitment.

Mr. Lander wants hospitals to consider a patient’s history when deciding whether to admit them and to allow nurses to be able to evaluate individuals for involuntary hospitalization, among other changes.

Mr. Adams, a former police officer who ran for mayor on a public safety platform, has taken a tough stance on clearing the streets of homeless people, but data shows that the population has grown. In January 2022, just after Mr. Adams took office, the city estimated that there were about 3,400 people living in streets and subways.

Another measure of street and subway homelessness is the number of unsheltered people on the caseload of outreach workers. That, too, has gone up under Mr. Adams, to about 3,250 in June 2024, from about 2,050 in June 2021.

Mr. Lander, when asked how he could fix the problem when so many other elected officials have struggled, cited his experience leading a housing nonprofit and his singular focus on the issue. He said he would ask his staff for weekly updates on the city’s “by name list” of people who are homeless to make sure they were on a path to housing.

“I’m making this my No. 1 promise to New Yorkers, and it will be my No. 1 focus when I become mayor,” he said.

Jan Ransom and Amy Julia Harris contributed reporting.