Nearly a dozen fire vehicles responded to the blaze Friday night in a six-story building in the Bronx, The New York Times reported.
The dead children were identified as Elijah Artis, 5; Jeremiah Artis, 2; and Michael Turner, 4 months. Two girls aged 4 and 4 months, and a 25-year-old woman, were treated for smoke inhalation.
The woman and a toddler fled the apartment on the fire escape. A neighbor said she tried to re-enter the apartment, but was turned back by heavy smoke. Another person rescued another child.
FDNY spokesman Daniel Glover said the fire was accidental, caused by a candle in the kitchen area of the apartment.
Consolidated Edison spokesman Allan Drury told CNN the apartment's electricity had been turned off two days earlier.
"The account had a significant amount of arrears -- well into the thousands of dollars," he said. "We try to avoid turning service off to customers. We'll put them on payment plans to work with them to avoid turnoff, but this account had substantial arrears."