The 15-year-old building housing about 200 people - mostly migrant workers and their families - collapsed Monday evening into a mountain of concrete slabs, iron rods, bricks and mortar in New Delhi's Lalita Park neighborhood.
About 30 people were believed still trapped under the rubble, said New Delhi's top elected official, Sheila Dikshit, and emergency efforts were hampered because fire engines had difficulty navigating the neighborhood's narrow alleyways.
At least 51 people were killed and 76 injured, said Rajesh Kumar, a spokesman of the Delhi Fire Service.
Local residents who were first to arrive at the accident site used bare hands to scoop away debris until they were joined by police and firefighters, who used gas cutters to cut through the iron rods. Police brought in sniffer dogs to locate people trapped under the debris.
Residents helped carry the injured to vehicles and to transport them to nearby hospitals, as hundreds of people crowded around or peered down from rooftops of nearby buildings.
Dikshit said it was not immediately possible to say what caused the accident but said there would be an inquiry.
"The scale of the tragedy is unprecedented. I don't think such a tragedy has taken place in Delhi in the recent past," the Press Trust of India news agency quoted her as saying.
New Delhi's finance minister, A.K. Walia, told Press Trust of India that this year's unusually heavy monsoon rains could have weakened the building's foundation. He said floodwaters of the Yamuna River had inundated the area two months ago.
Residents said rainwater had accumulated in the basement of the building, but it was not immediately clear if it had been pumped out.
Police said they were searching for the building's owner, identified as Amrit Singh, a building material trader.
Poor construction material and inadequate foundations often are blamed for building collapses in India. In New Delhi, where land is at a premium, unscrupulous builders often break building laws to add additional floors to existing structures.