The deceased was identified as Harish, 43, while the family members injured were his mother Amrit Devi, 65, Sunil, 47, Gyanshyam, 28, Neha, 18, Abhishek, 12 and six year-old Anant.
The condition of three of them was said to be critical.
"Harish's neighbour informed Delhi Fire Services after which three fire tenders were rushed to the spot and the blaze doused at 6.50 am," said a fire officer.
"Hearing his mother's cries for help, Harish had rushed downstairs. While rescuing her, he received over 80 per cent burn injuries and died on the spot," the officer said.
Firefighters and police faced difficulty in dousing the fire and rescuing the injured due to the narrow approach pathway to the building, he added.