FDNY Commissioner Daniel Nigro said the fire started in the kitchen of a first-floor apartment as a 3-year-old boy was playing with the burners.
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The boy's mother was alerted to the fire by the boy screaming, Nigro said. She escaped the apartment with her kids but left the front door open.
Nigro said this caused the fire to spread to the rest of the building very quickly by traveling up the stairs. It acted like a chimney and people in the rest of the building had very little time to react.
Mayor Bill de Blasio called it a "horrible, tragic accident."
"Children starting fires is not rare," Nigro said, adding that the city has a program to educate the public about fire safety. He said that if there is a lesson to be learned from this tragedy is that if you have an apartment fire you must close the front door.
De Blasio said Friday on WNYC that four people are still fighting for their lives following the fire Thursday night in the Bronx.
The New York Police Department says those who died include girls ages 1, 2 and 7, and a boy. His age was not given.
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The 5-alarm fire broke out just before 7 p.m. on Prospect Avenue near East 187 St. on the first floor of the five-story building. FDNY firefighters arrived at the scene within three minutes.
The flames quickly spread up to the fifth floor. The building is described as "non-fireproof" and was highly combustible.
MORE: What we know about the victims of the NYC apartment fire
The fire was brought under control just after 9 p.m. The scene was described as having a very heavy smoke condition. The victims perished on every floor of the building.
Investigators initially pointed to a natural gas line as possibly fueling the fire and causing it to spread quickly, but officials with Con Edison said there is no indication natural gas was involved in the fire.
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More than 170 firefighters responded to the scene.
"In a department that's certainly no stranger to tragedy we're shocked by this loss," FDNY Commissioner Daniel Nigro said.
The Office of Emergency Management and the MTA sent buses to the location to accommodate residents that have been evacuated from the building.
"Based on the information we have now, this will rank as one of the worst losses of life to a fire in many, many years," De Blasio said during a press conference at the scene.
PHOTOS from the scene: