The fire broke out on the fifth floor of the building in Harlem at the intersection of Adam Clayton Powell Boulevard and 142nd Street at about 1:45 a.m. on Wednesday.
Officials said that all six people -- two adults, two boys and two girls -- were from the same family. All were pronounced dead on the scene.
The children range in age from 3 to 11, the fire department said. One of the adults is the children's mother, while the second adult is her stepbrother.
The fire did not appear to be suspicious, but an investigation is underway, fire officials said. Early indications are that the burn on the stove may have been left on overnight, a source told ABC News.
"Units were met at the door of that apartment with fire. The entire apartment was involved," Fire Commissioner Daniel Nigro said. "They aggressively moved in, extinguishing the fire as they did. When they reached the two rear bedrooms we found six occupants of that apartment deceased."
It took about an hour to get the fire under control, Nigro said.
"As aggressive as those members could be, they were not able to reach those occupants," Nigro said of his firefighters.
The building is part of the Frederick E. Samuel Houses, a city-owned housing complex.