Two others, including the girl's mother, were injured and hospitalised.
According to the Delhi Fire Services, a call was received at 3 am about the blaze which started on the ground floor and subsequently spread to the other floors of the building. The cause of the fire is suspected to be an electric short- circuit.
Eight fire tenders took one hour to douse the blaze.
The bodies of 12-year-old Harshu, her father Sanjay Verma (40), grandfather Vijay Verma (63) and brother Chiku (four) were found on the staircase.
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Police suspect the Verma family tried to get out of their second-floor apartment, got caught in the flames and smoke on the stairs and died of suffocation.
They said the fire was not a "major" one, and there would have been no casualties, had the Verma family stayed indoors or parked themselves on the balcony.
The other occupants of the building, which houses 11 flats, either stayed on their balcony or rushed to the rooftop to escape the fire.
Harshu's mother Mona (34) was undergoing treatment at the GTB Hospital.
Another woman, Binesh Rathi (40) who lives in a first- floor flat, jumped off the balcony and suffered injuries. She was admitted to a private hospital.
Shankar, who stays on the top floor of the building, recalled how in a matter of few seconds, happiness changed into sadness.
Shankar runs a call centre from his home and was awake when he saw flames emananting form the ground floor.
"I rushed out to see what was happening and found a couple of bodies on the staircase. One of the bodies was of a child and I immediately took the child to a hospital with assistance from the police personnel. But he was declared brought dead in the hospital," he said.
"Those last moments when I saw the brother-sister duo together would continue to haunt me forever," Shankar said.
He said the fire started in the electric metre box in the gallery and spread to the motorcycles and scooters parked nearby.
The Verma family had been staying in the building for the last seven-eight years and were cordial with everyone. They were in the transport business.
Meanwhile, an official from the Delhi Fire Services said the rescue work was delayed as fire tenders could not move smoothly due to congested lanes.