A 76-year-old man died on Friday after being shoved down the stairs at the 18th Street subway station in Manhattan, and the police arrested a suspect who had been arrested multiple times in recent months and had been discharged from Bellevue Hospital’s psychiatric ward just hours before.

The victim, Ross Falzone, landed on his head at the bottom of the stairs and suffered a traumatic brain injury, a fractured spine and a fractured rib after a stranger rushed forward and pushed him, the police said.

Mr. Falzone had been walking north on Seventh Avenue toward the subway station in the Chelsea neighborhood on Thursday evening, said Brad Weekes, assistant commissioner of public information for the Police Department. Walking about 30 yards behind him was the stranger, according to surveillance footage from the scene, Mr. Weekes said. As Mr. Falzone reached the station, the man rushed forward and pushed him down the stairs. He was taken to Bellevue where he died shortly before 3 a.m. on Friday.

The death sparked outrage at City Hall. Mayor Zohran Mamdani quickly called for an investigation into how Bellevue handled the discharge of the suspect and suggested that institutional problems at the hospital might have led to the random attack.

“I am horrified by the killing of Ross Falzone and the circumstances that led to it,” Mr. Mamdani said in a news release on Friday, in which he ordered “an immediate investigation on what steps should have been taken to prevent this tragedy.”

Police identified the suspect as Rhamell Burke, 32.

In the three months preceding the attack, Mr. Burke was arrested four times, Mr. Weekes said, including an arrest on Feb. 2 in connection with an assault on a Port Authority police officer.

Mr. Burke’s most recent interaction with the police began at around 3:30 p.m. Thursday, when he approached a group of N.Y.P.D. officers outside the 17th Precinct station house on East 51st Street, Mr. Weekes said. He grabbed a stick from a pile of garbage on the street and approached the officers, who told him to drop the stick. When he did, officers placed Mr. Burke in a police vehicle and drove him to Bellevue, where he was admitted to the emergency room at around 3:40 p.m., Mr. Weekes said. Mr. Burke was taken to the hospital’s Comprehensive Psychiatric Emergency Program for evaluation and treatment, Mr. Weekes said, and was released from the hospital one hour later.

He was just a mile and a half from the hospital when he encountered Mr. Falzone at around 9:30 p.m. Thursday.

On Friday afternoon, police officers found Mr. Burke in Penn Station, where they arrested him. He was in custody on Friday evening. It was unclear Friday if Mr. Burke had a lawyer.

The mayor said he had requested help from the New York State Department of Health, which will investigate the decision to release Mr. Burke from Bellevue and conduct a review of similar cases at the hospital. The state agency also will investigate psychiatric evaluation and discharge procedures across NYC Health and Hospitals, the city’s public hospital system, according to the news release.

Mr. Falzone was a retired high school teacher who lived alone for many years in an apartment building on the Upper West Side. His friends were in shock on Friday about his death. They shared memories of an affable but private man who rarely spoke about his family or personal life.

Mr. Falzone had been recovering from a recent surgery and seemed more mobile and happy, said Marc Stager, 78, Mr. Falzone’s next-door neighbor on a tree-lined block of West 85th Street. He was known as a cheerful “yapper,” said Briel Waxman, a neighbor. He was the kind of New Yorker who enjoyed chatting with neighbors about historical details of his building and seeing performances at Lincoln Center with friends.

“He was always out and about,” said Ms. Waxman, 35, who often returned to her apartment at midnight or 1 a.m. to find Mr. Falzone arriving home at the same time. “I was like, ‘I don’t know if I’m proud of you or embarrassed of myself,’” she remembered telling him.

Mr. Falzone had wide taste in music — opera, classical, jazz, pop — and neighbors could tell he was home when they heard notes escaping from under his apartment door, Mr. Stager said.

He was “a helpless old guy,” said Mr. Stager, who added that he was “disappointed and shocked, frankly, that somebody could do such a thing” as shove such a defenseless person down the stairs.

When Ms. Waxman moved into the building five years ago, Mr. Falzone was among the first people to welcome her, she said. He once brought a package to her door that had been delivered to the wrong unit and shared that what is now a blank wall in her apartment had once been a fireplace.

Ms. Waxman sat in her living room on Friday and cried as she talked, dabbing her eyes with a tissue. She remembered Mr. Falzone as “just overall, nice, talkative, genuine human.”