A 40-year-old woman was shoved to her death in front of a subway train on Saturday morning at the Times Square station, the police said, an apparently random attack that came amid a fear of increased crime rates in a transit system struggling to regain ridership during the pandemic.

The woman was standing on the platform around 9:30 a.m. waiting for the train to arrive at the station at 42nd Street in Manhattan, the police said. As a Brooklyn-bound R train pulled into the station, a man pushed her onto the tracks, and she was struck.

She died at the scene, the police said. Her name was not released on Saturday. The woman was Asian. But the police said the attack might have been random, and there was no indication that she had been targeted because of her race or ethnicity.

The man identified by the authorities as the one who pushed her onto the tracks turned himself in to the police about 30 minutes later. The police said the man, Simon Martial, 61, was homeless and has had at least three previous encounters with the authorities related to mental health problems. He was charged with murder on Saturday evening.

Mayor Eric Adams said at a news conference at the subway station on Saturday that the “senseless act of violence” was a stark example of the immediate need to tackle what he called a mental health crisis in the subway system.

“Our hearts go out to the families who are impacted,” Mr. Adams said. “To lose a New Yorker in this fashion will only continue to elevate the fears of individuals not using our subway system.”

The killing on Saturday lies at the crux of several issues that have prompted concerns from some New Yorkers over subway safety since the pandemic began. It came after an announcement this month by state and city officials of changes to how the police would operate in the transit system and work with homeless people as officials try to lure back more riders.

Unprovoked attacks on Asian Americans during the pandemic, including several in the subway system, have also stoked fear and anger in New York and elsewhere, with activists and elected officials pointing both to mental illness and to the impact of rhetoric blaming the coronavirus on China.

Keechant Sewell, the police commissioner, said on Saturday that whether the killing was a hate crime remained under investigation. But, she added, based on initial information, the episode appeared to have involved someone who was troubled.

Minutes before the woman was pushed, Mr. Martial confronted another female rider, who was not Asian, police officials said. That passenger later told the police that she believed that Mr. Martial intended to push her onto the tracks.

Afterward, Mr. Martial rode into Lower Manhattan, the police said. He told officers at the Canal Street station that he had pushed a woman in front of a train and was taken into custody.

He has several prior arrests, including one for a robbery for which his parole term had recently ended, the police said.

Elected officials said the killing on Saturday underscored the importance of a more well-rounded approach to matters of safety, homelessness and mental health regarding the subway system.

U.S. Representative Grace Meng, Democrat of Queens, added that even if the police determined that the attack was random, the killing had inflamed the safety concerns that some in Asian communities have faced during the pandemic.

The numbers of bias incidents against New Yorkers in the subway system have been elevated in recent months. An Asian woman was killed in July at a Manhattan subway station when a man pulled her down a set of stairs during a robbery attempt, though the attack was not deemed to have been racially motivated.

“Too often Asian Americans are seen as foreigners and people who are not truly American,” Ms. Meng said. “This has been a really tough year and a half for the Asian American community.”

Gov. Kathy Hochul and Mr. Adams have said that the more than 2,000 officers who are assigned to patrol the system will lead more frequent sweeps of subway platforms and trains as they attempt to ease broad concerns over crime.

The state also plans to develop small teams of social workers and medical professionals to provide services as homelessness on the streets and subways persists for thousands. Officials have said that transit officers will make referrals to those teams, with an aim of better addressing the needs of people who are homeless or who have mental illnesses.

Mr. Adams said that occurrences like the one on Saturday fostered a perception of elevated crime that had prompted worries among some subway riders.

Transit officials have emphasized that serious crimes in the system are at their lowest levels in decades and that major felonies were at their lowest combined total in 25 years through November. However, ridership was also much lower, and the rates of several violent crimes have risen since 2019.

Three murders were reported in 2019 in the system; that number doubled to six in 2020. Through November, six murders had also been reported in 2021.

Other episodes, such as assaults, stabbings and the shoving of people onto tracks, have also generated a drumbeat of news reports about violence that transit officials say have fed the fears.

Canella Gomez, the vice president of a union that represents train conductors and operators, said in a statement that she had spoken with the man who was operating the train that struck the woman on Saturday.

“No train operator comes to work expecting to have a passenger thrown in front of his or her train,” Ms. Gomez said. “This is the part of the job that no one is ever truly physically, mentally or emotionally prepared for.”

Michael Gold contributed reporting.