Rescuers worked through the night to remove the rubble of a collapsed century-old apartment building in India's financial capital of Mumbai where at least 33 people have died and nearly a dozen others may still be buried.

Fire officer Prabhat Kumar said on Friday that 15 injured survivors have been pulled from the debris so far.

Police said 33 bodies had been recovered from the rubble by early Friday, and hope was fading of finding anyone alive more than 24 hours after the building collapsed.

Authorities have no clear idea how many people lived there or were in the ground floor work spaces.

But police say nearly a dozen people are missing and feared trapped beneath the huge mound of broken concrete slabs and twisted steel girders.

Rescuers used earth-moving machines to lift concrete slabs and cement blocks as they searched for survivors.

The office of Indian Prime Minister Narendra Modi tweeted condolences, saying the event was "saddening".

Thousands of buildings in Mumbai are more than a century old, their foundations weakened by years of heavy monsoon rains.

The collapse of a four-storey building in the city's suburb of Ghatkopar last month killed 17.

Ageing building

The rickety five-storey building - which is at least 110 years old - in the congested Bhendi Bazaar area of south Mumbai had been declared unsafe to live in six years ago, but some people continued to stay there.

The residents of an adjacent building were advised to leave after it developed cracks following the collapse.

The collapsed building had housed nine families in apartments above a first-floor nursery school, but the collapse Thursday morning occurred before the toddlers had arrived for the day, police said.

The ground floor had warehouses where workers may have been present.

Nearby resident Amina Sheikh tightly held her four-year-old grandson's hand as they watched the rescue efforts from a safe distance.

"This is my grandson. He used to go to school in that building," she said, tearfully pointing at the rubble.

She had been getting the boy ready for school when she heard a loud boom and saw the building had come crashing down.

It was "an hour before his class began. That's why my grandson's life was saved", she said.

It was the first major building collapse after Mumbai recorded 315-mm (12 inches) rainfall on Tuesday, the city's highest since 2005.

Monsoon season

Building collapses are common in India during the monsoon season, which is June to September.

High demand and lax regulations encourage some builders to use substandard materials or add unauthorised extra floors.

Property prices and rents in Mumbai are among the highest in India as the city has expanded in the past five decades.

The city is slowly returning to normal after being paralysed by heavy downpours for two days. Train services and public transport were disrupted by flooding and water seeped into many low-lying buildings.

The city struggles to cope with the monsoon deluge each year, drawing criticism about its poor planning.

Since the start of the season, devastating floods across South Asia have killed more than 1,000 people and affected close to 40 million across northern India, southern Nepal and northern Bangladesh.

The rains have led to flooding in a broad arc stretching across the Himalayan foothills in the three countries, causing landslides, damaging roads and electric towers and washing away tens of thousands of homes and vast swaths of farmland.

The rains moved into Pakistan on Thursday, with the heavy downpour flooding streets in Karachi. At least eight deaths were considered flood-related.