The Ramirez children, four boys and two girls aged three to early teens, died in the third-story apartment as firemen rescued their mother and three other siblings, Fire Commissioner Raymond Orozco said.
It was "obviously a very tragic day for this family," commissioner Orozco said.
According to commissioner Orozco, the mother and her nine children had been using candles to light the three bedroom apartment for several weeks because they did not have electricity.
"There were no working smoke detectors in the apartment," he added.
A total of nine people were rescued from the building, but several children went into cardiac arrest after they were pulled out of the apartment, Fire Department spokesman Larry Langford said.
According to media reports, the mother and her surviving children were taken to hospital for treatment.