A man has been arrested in New York in connection with the death of a woman who was set on fire on a subway train in Brooklyn.

Police Commissioner Jessica Tisch described the incident on Sunday as "one of the most depraved crimes one person could possibly commit against another human being".

She said the woman was on a stationary F train to Brooklyn when she was approached by a man who used a lighter to ignite her clothing.

The victim died at the scene, she said, adding that the suspect had been arrested following a tip-off from a group of high school students as he rode the subway later on Sunday.

Police said the woman, who has not been named, was in a subway carriage at the Coney Island-Stillwell Avenue station in Brooklyn at about 07:30 local time (12:30 GMT) when a man approached her.

There was no interaction before the attack, police said, adding that they did not believe the two people knew each other.

The man got off the train as police officers on patrol in the station rushed to the fire.

"Officers were on patrol on an upper level of that station, smelled and saw smoke and went to investigate," Ms Tisch said.

"What they saw was a person standing inside the train car fully engulfed in flames."

Police are still working to identify the victim and the motive for the attack.

"Unbeknownst to the officers who responded, the suspect had stayed on the scene and was seated on a bench on the platform just outside the train car," Ms Tisch added.

She explained responding officers were able to get a "very clear, detailed" look at the man and images were disseminated by the New York Police Department (NYPD).

Later, three high school-aged New Yorkers called 911 to report they recognised the suspect on another train, Ms Tisch told reporters.

The man was then located after officers boarded the train and walked through the subway carriages.

He was arrested at Herald Square station - which is located in near to the Empire State Building in Manhattan.

The man was found with a lighter in his pocket, the police commissioner said.

"I want to thank the young people who called 911 to help," Ms Tisch added.

"They saw something, they said something and they did something."

Gulotta explained detectives are still trying to establish whether the victim was asleep when she was set on fire.

"She's definitely there, she's motionless," Mr Gulotta added.

"So to say if she's asleep or not, we're not 100% sure, but it appears that she's motionless at that spot.

"There is no interaction between the two. And when the incident happens, there is no interaction between them." (BBC)

?PHOTO: Police were called to Coney Island-Stillwell Avenue Station in Brooklyn after a woman on a subway car was set on fire. PHOTO: Getty Images.

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