Police have arrested a man for allegedly setting a sleeping woman in a New York subway on fire and then watching her burn to death.

The incident occurred on Sunday at about 7:30 a.m. on an idling F train at the Coney Island-Stillwell Avenue station.

NYPD Commissioner Jessica Tisch was quoted as saying by New York Post: "As the train pulled into the station, the suspect calmly walked up to the victim, who was in a seated position at the end of a subway car … and used what we believe to be a lighter to ignite the victim’s clothing, which became fully engulfed in a matter of seconds."

Tisch described the deceased woman as 'innocent'.

Patrolling policemen tracked the woman and doused the flame.

However, the victim could not survive.

“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,” Tisch said.

“The body-worn cameras on the responding officers produced a very clear, detailed look at the killer," Tisch said.

Later in day, three high schoolers called police to say they saw the man pictured in images released by the NYPD at the Jay and York Street station on the F line, Tisch said.

Police recovered a lighter from the pocket of the suspect when he was detained.

Officials told New York Post the 33-year-old suspect came to the US in 2018 from Guatemala.

He was detained by border patrol agents in Arizona in June of that year, sources told the newspaper.

The identity of the victim is still not known.

New York Mayor Eric Adams described the incident as 'senless'.

"Grateful to the young New Yorkers and transit officers who stepped up to help our NYPD make a quick arrest following this morning's heinous and deadly subway attack," he said.

Adams said: "This type of depraved behavior has no place in our subways and we are committed to working hard to ensure there is swift justice for all victims of violent crime."

"My prayers are with the family of the victim in this senseless killing," he said.