"It's been more than three days, so we don't know if there are any survivors any more, but we are not losing hope," Satya Pradhan, the head of the National Disaster Response Force, told Reuters. At least eight people are still missing and rescue personnel are clearing debris to look for them, said Pradhan.
The building, a three-story structure in a narrow alley of the industrial town of Bhiwandi, on the north-east outskirts of Mumbai, collapsed early on Monday.
Rescue work has been hampered by rain and a narrow entrance to the alley, which prevented heavy equipment from being brought in to clear debris.
Officials are still investigating the cause of the collapse of the structure, which housed 54 apartments.
Such disasters are commonplace in India during the monsoon season, as the torrential rains can destabilize old and often illegally constructed buildings. This week's collapse however, is one of the worst such incidents in recent years around Mumbai.
Last month, more than a dozen people were killed when a building collapsed in the industrial town of Mahad, 165 km south of Mumbai.
In 2013, more than 120 people were killed in two separate building collapses around Mumbai.