Two others, including the girl's mother, were injured and admitted to a city hospital.
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.
Police said it was Harshu's birthday.
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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.
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.
An official from the Delhi Fire Services said that the rescue work was delayed as fire tenders could not move smoothly due to congested lanes.