At least 21 people have died and several more were feared trapped after an old building due for demolition collapsed in India's financial hub of Mumbai on Thursday following torrential rains.

Rescuers were searching for survivors at the site of the collapsed five-story building, believed to be about 117 years old, in the busy Bhendi Bazar market area.

"More bodies have been pulled out from under the debris, taking the toll to 21," Rashmi Lokhande, an officer at the Brihanmumbai Municipal Corporation disaster control unit told DPA by phone.

She said 13 more people were injured and were taken to nearby hospitals.

"The rescue work is in its final phase and will continue till late Thursday night. We estimate that about 10 to 12 people might still be trapped under the rubble," Lokhande added.

"Eighteen people have died. Another 12 have been admitted to hospital," Vijay Khabale-Patil, a spokesman for Mumbai's civic authority, told AFP.

Officials estimated that up to 40 people could have been caught up in the disaster. Khabale-Patil said rescue operations would go on into the evening.

Ambulances rushed the injured to the nearby J.J. Hospital in the south of the city while locals joined a 43-member National Disaster Response Force team in picking through piles of debris in a desperate hunt for survivors.

Local police, teams from the National Disaster Response Force and fire services officials were involved in the day-long operations.Firefighters and rescue workers search for survivors at the site of a collapsed building in Mumbai, India, August 31, 2017 (Reuters Photo)Bhendi Bazar in southern Mumbai is a predominantly Muslim area that, like much of the city, is highly congested, packed with shops, restaurants, food stalls, precarious century-old buildings, tenement blocks and new developments for luxury apartments.

The collapsed building had been marked for demolition as part of a $600 million redevelopment project that is replacing hundreds of ramshackle, decades-old low-rise buildings with around a dozen glitzy new tower blocks.

As rescuers struggled to remove the concrete slabs to reach survivors underneath, the desperate relatives of those trapped pleaded with officials to speed up operations.

"There was a massive bang. We couldn't see anything due to the dust and smoke. Once the dust settled, we realized it was a building collapse," Amina Sheikh, a local resident told broadcaster NDTV.

The building collapsed after Mumbai was lashed by its heaviest rains in 12 years on Tuesday, which killed at least 11 people.

Police and local agencies suspect that heavy rains could have weakened the building, leading to its collapse.

Local media reported that a larger tragedy was averted as the building housed a playschool, which was closed at the time of the collapse. Building collapses are common in Indian cities, particularly during the monsoon season.

State chief minister Devendra Fadnavis told reporters that the building was deemed unsafe by local authorities a couple of years ago.

"Residents should have [evacuated] the building as it was due for demolition in May 2016. We have ordered a probe and strict action will be taken against those guilty," he said.

Local legislator Amin Patel told reporters that the building was over 100 years old and was on a list of 800 precarious structures listed as "dangerous" by civic agencies.

Tuesday's rains in Mumbai brought the metropolis with 18 million inhabitants to a standstill as the city was placed on high alert after road, rail and air traffic were disrupted.

Seven coaches of a passenger train were derailed near Mumbai due to a landslide, but there were no injuries.

Millions are forced to live in cramped, ramshackle properties because of spiraling real estate prices and a lack of housing for the poor.

Activists say housing societies, private owners and builders often cut corners to save on costs.

Rent control acts mean landlords cannot afford to maintain buildings while poor people choose to remain in homes even after they have been declared unsafe because they have nowhere else to go.

"Most of the buildings in Bhendi Bazaar are old and dilapidated. We always live in fear that they will collapse during monsoons," 63-year-old Mohammed Shaikh told AFP.

In July, 17 people including a three-month-old baby died when a four-story building gave way in the northern suburb of Ghatkopar.

In 2013, 60 people were killed when a residential block came crashing down in one of Mumbai's worst housing disasters.

On Thursday officials in Mumbai said the death toll from floods in and around the city were expected to rise above 10 as the waters receded.

"We are still on the lookout for more missing persons and the number may go up," Santosh Kadam, spokesman for disaster control in Thane, told AFP.

More than 1,200 have been killed India, Nepal and Bangladesh in devastating floods this monsoon season.