A 38-year-old Brooklyn man was fatally stabbed early Friday after he and another man began fighting on a downtown No. 5 train in Manhattan during the morning rush hour, officials said.

The men began to argue after one stepped on the other’s shoe, according to a law enforcement official.

As the train headed toward the Brooklyn Bridge-City Hall station, the assailant stabbed the man, the law enforcement official said. When the train stopped at the station, the men got off and the attacker stabbed the victim a second time, the official said.

Officers responding to a 911 call about a stabbing at the station arrived at around 8:30 a.m. to find the victim, John Sheldon, unconscious on the platform with several chest wounds, the police said. Emergency medical workers took Mr. Sheldon to Bellevue Hospital, where he was pronounced dead. (The Police Department initially identified the victim as Sheldon John.)

The assailant, believed to be in his 30s, fled from the station, the police said. The investigation was continuing, and no arrests had been made as of Friday afternoon, the police said.

The police said they did not believe the two men knew each other.

At 10:15 a.m., a splatter of what appeared to be blood was visible inches from the edge of the station’s downtown platform. Officers milled about the blocked-off platform, as downtown trains, diverted from the station amid the investigation, rumbled past. Riders on the uptown side looked on, stunned and confused.

The killing, the first on the subway this year, came at a fraught time for the Metropolitan Transportation Authority, the state agency that operates the subway and is in a standoff with the Trump administration over funding for the transit system.

Sean Duffy, the transportation secretary, has waged a public campaign since February deriding the subway system as lawless and dangerous, and threatening to withhold federal money unless the M.T.A. addressed crime in the system.

But crime on the subway has declined, a trend that Jessica Tisch, the city’s police commissioner, has attributed to the deployment of additional officers on platforms and trains.

Major crime on the subway fell 18 percent in the first three months of the year, according to Police Department data. For the first time in seven years, there were no murders in the transit system in the year’s first quarter.

As of last Sunday, overall crime in the system was down almost 11 percent compared with the same period last year, although it has begun to rise slightly in recent weeks.

Still, after a series of random and jarring attacks in the system over the past two years, transit officials have struggled to dispel a persistent belief among some riders that the subway is unsafe. The killing on Friday was likely to add to that perception.

Some people have criticized the number of officers now patrolling the system, but Elizabeth Daley, who was waiting for a train on the uptown platform Friday morning, said she would like to see more.

“A lot of the time I would rather take a 30- or 40-minute walk just because once you’re in there and it’s moving, you can’t really get out,” Ms. Daley, 20, said.

Others shrugged off the episode, describing it as unsettling but not unusual.

“Obviously it freaks me out, but it’s New York. It’s a normal thing,” said Jonathan Ricket, a 19-year-old Pace University student who lives in Newburgh, N.Y., and commutes into the city daily for classes.

He paused for a moment.

“I’m just glad I didn’t see it,” he added.