Rescue workers in Mumbai searched for more than 30 people feared trapped beneath a collapsed building on Thursday, following two days of torrential rain in India's commercial hub.

One body had been found and a second victim was later declared dead at hospital, while eight survivors had been pulled from the rubble, a police official told the media as rescue operations continued.

A police official told Reuters nine families were living in the building, which is located in Mumbai's Dongri neighbourhood, an area full of narrow streets with closely packed buildings, some nearly a century old.

Television images showed people on top of the debris, looking for those trapped as rescue personnel reached the spot.

"Rescue operations are already underway. We have sent 12 fire brigade vehicles to the spot. Ambulances are also ready to take the victims to the hospital," the fire control room official said.

A National Disaster Response Force (NDRF) team was also involved in the rescue operations.

Police suspected the heavy rains that lashed the could have weakened the building.

Last month, 17 people were killed when a four-storey building collapsed in an eastern suburb of Mumbai.