The dead included a child around a year old, New York City Mayor Bill de Blasio said during a briefing outside the building.
“We may lose others as well,” he added.
Fire Commissioner Daniel Nigro called the fire, “historic in its magnitude,” because of the number of lives lost.
Excluding the Sept. 11 attacks, it was the worst fire in the city since 87 people were killed at a social club fire in the Bronx in 1990.
“Our hearts go out to every person who lost a loved one here and everyone who is fighting for their lives,” Nigro said.
The blaze broke out on the first floor of a five-story building just before 7 p.m. and quickly ripped through the roughly century-old structure, which stands in a row of similar apartment buildings a block from the grounds of the Bronx Zoo.
Tenants of the building, a mix of native New Yorkers and Latino and African immigrants, scrambled down fire escapes. But the flames moved so fast, spreading through every floor of the building within minutes, that many never made it out of their apartments.
The cause remained under investigation.
About 170 firefighters worked in bone-chilling cold, just 15 degrees, to rescue about a dozen people from the building. Water sprayed from hoses froze on the street.
Thierno Diallo, 59, a security guard originally from Conakry, Guinea, who lives in a ground floor apartment said he was asleep when he heard banging on the door. It took him a moment to realize what was happening.
“Only when I heard people screaming, `There’s a fire in the building!”’ he said. “I heard somebody, `Oh! Fire! Fire! Fire!”’
He ran out in his bathrobe, jacket and sandals.
Kenneth Kodua, 37, said he left his apartment to get food, leaving his roommate behind, and came back to find people fleeing in a panic.
Hours later, he was still trying to find out whether his roommate escaped.
“I tried calling her. I tried calling. No answer,” he said, still clutching his bag of uneaten food. His phone was dead.
Many questions remained in the immediate aftermath of the blaze, including how the fire spread so quickly in a brick building built after catastrophic fires at the turn of the 20th century ushered in an era of tougher enforcement of fire codes.
The building had more than 20 units. It was not new enough that it was required to have modern-day fireproofing, like sprinkler systems and interior steel construction.
Neighbourhood resident Robert Gonzalez said a friend who lives in the building was able to get out via the fire escape as another resident fled with five children.
“When I got here, she was crying,” Gonzalez said.
Other witnesses described seeing burned bodies being carried away on stretchers and young girls who had escaped the building standing barefoot outside with no coats.
Windows on some upper floors were smashed and blackened. Displaced residents wrapped in Red Cross blankets were staying warm on city buses, brought in to provide heat.
The death toll surpassed the 10 who died, including nine children, in a four-story home in another part of the Bronx in 2007. That blaze had been sparked by a space heater.
Twum Bredu, 61, arrived in the neighbourhood looking for his brother, who had been staying with a family in the building. The family, a husband and wife and four children, got out. But there was no word yet about his brother.
“I’ve been calling his phone, it’s ringing, but nobody picks up,” Bredu said. “He was in his room, and we don’t know what happened.”