The Manhattan borough president on Tuesday announced a plan that he said will help expand access to psychiatric care and housing for severely mentally ill homeless people in New York City.

The proposal by the borough president, Mark Levine, was designed to address gaps in New York City’s social safety net in the wake of several high-profile incidents involving random attacks by homeless people with mental illness.

It calls for the creation of 240 long-term psychiatric beds in the public hospital system’s extended care units, where patients can be stabilized rather than discharged onto the streets, and the addition of intensive mobile treatment teams to care for those patients outside the hospital setting. Mr. Levine wants the city to double the number of those teams to 62, which would allow them to serve about 1,500 people. As of August, nearly 480 people were waiting to be assigned to such a team, records show.

“We have not invested in the kinds of interventions that put people back on the right path,” said Mr. Levine, a former city councilman who took office as borough president last year. “I am optimistic if we have the will we can get this right.”

Mr. Levine unveiled his plan in the wake of a New York Times investigation that identified breakdowns in the city’s mental health care system — homeless shelters, hospitals, specialized treatment teams and other organizations. The lapses preceded nearly 100 acts of violence over the past decade, The Times found, sometimes by a matter of days or hours.

Mr. Levine said the killing of a financial consultant early last year by a homeless man with schizophrenia and a history of erratic behavior prompted him to take a hard look at the gaps in mental health care, and what he described as a “crisis playing out on the streets of New York City.”