The cause of the blaze -- the city's deadliest in decades -- was under investigation, authorities said.
The fire broke out around 6:51 pm (2351 GMT) Thursday in a 25-apartment building near the Bronx Zoo, one of the most popular tourist attractions in the US financial capital.
Fueled by strong gusts of frigid wind, the flames quickly raced through the building.
More than 160 firefighters rushed to the scene and took some three hours to control the blaze, local media reported. In the bitter cold, water leaking from the hoses froze on the pavement.
Three girls -- aged one, two and seven -- and an unidentified boy were among the dead, police said Friday. A 19-year-old woman was also killed.
Tearful residents said they heard cries of "fire, fire" in the building followed by a mad rush to exit the smoke-filled building. Many fled into the frigid night with just the clothes on their backs.
The cause of the fire has yet to be determined. The plaster and brick structure, built in 1916, was not fireproof and had six open violations including for a defective smoke detector, New York Times reported.
Mayor Bill de Blasio called it an "unspeakable tragedy," in the middle of the holiday season, as the city of 8.5 million straddles Christmas and New Year festivities.
"Tonight here in the Bronx there are families that have been torn apart. This is the worst fire tragedy we have seen in this city in at least a quarter century," de Blasio told reporters after fire fighters extinguished the flames.
De Blasio said 12 people died in the fire, and four people were critically injured.
The blaze began on the first floor and spread rapidly throughout the five-floor walk-up on Prospect Avenue, with fire fighters on the scene within three minutes, department chief Daniel Nigro told reporters.
Fire fighters plucked panicked residents to safety from a fire escape.
Two of the dead were discovered in a bath tub full of water, where they had apparently sheltered from the blaze, US media reported.
Nigro said it was "way too early" to comment on the cause of the inferno.
"This tragedy is, without question, historic in its magnitude," said Nigro.
"People died on various floors, they range in ages from one to over 50," he added. "In a department that's certainly no stranger to tragedy, we're shocked at this loss."
It was the second deadly New York residential blaze in less than two weeks. A mother and three children were killed when a fire tore through their Brooklyn home on December 18.
In March 2007, 10 people were killed in another Bronx fire, at the time the worst blaze in the city since 1990 apart from the September 11, 2001 terror attacks.
The late Thursday fire was New York's deadliest since 87 people were killed in a 1990 inferno at a Bronx social club, The Times said.
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