The father and two other children are still in critical condition.
Five other family members were injured in the early Monday blaze, including the father, three other children and a cousin.
Aliza Azan and three of her six children died in their home in a fire possibly caused by their Chanukah menorah.
The fire broke out inside a two-story home on East 14th Street just after 2 a.m.
According to the firefighters, the second floor was completely engulfed by the fire and it took nearly two hours for 80 firefighters to control it. The father, Yosef, was able to get two of their teenagers out of the house, but they are now in the hospital in critical condition.
"[The father] was able to get out of the second floor".
The investigation is ongoing. The FDNY is trying to figure out what sparked the fire.
Aliza, known locally as Luza, was the daughter of Rabbi Albert Hamra, a leader of the Syrian community in Israel, according to the New York Post. After spending many years in Holon, a city south of Tel Aviv, he moved to Brooklyn in the past year.
Police said the people killed were a 40-year-old woman and three of her children, an 11-year-old boy, a seven-year-old boy and a three-year-old girl.
Fire Commissioner Daniel Nigro described the incident as a complete tragedy, and says the fast-moving fire spread through open stairwells inside of the home preventing the family members from leaving.