Rescuers were desperately searching for up to 40 people feared trapped when a building collapsed in India's financial capital of Mumbai Thursday, officials said.

The four-storey residential building gave way around 08:40 am (0310 GMT) in the densely populated area of Bhendi Bazaar after heavy rains in the city that have killed 10 people.

"Forty people are believed to be stuck inside and a 43-member team is conducting rescue operations," an official for India's National Disaster Response Force (NDRF) told AFP.