Two toddlers were among at least six people who died after floods caused by heavy seasonal monsoon rains destroyed homes and disrupted traffic in India's financial capital, police said on Wednesday.

Train services resumed slowly and dozens of commuters began walking to work in Mumbai, a city of 20 million people that is home to India's two biggest stock exchanges and the headquarters of several major companies.

Some low-lying areas remained under water, causing vehicle pile-ups, after the city received nearly a month's equivalent of rainfall in a single day. Authorities ordered schools and colleges to shut following forecasts of more rain. 

"There are several stranded cars and two-wheelers on the roads that we are clearing," said traffic police official Amitesh Kumar.

"We are not expecting any major traffic jams as the machinery is geared up and the rain forecast is also not as bad."

Police said a 45-year-old woman and a 1-1/2-year-old child, members of the same family, died after their home in the northeastern suburb of Vikhroli crumbled late on Tuesday, while a 2-year-old girl died in a wall collapse.

In the neighbouring city of Thane, three people died after being swept away by floods, police added.

Several firms made arrangements to provide food and rest areas for employees stuck in offices, while officials of temples and religious bodies offered help to those stranded on streets.

Flights faced delays of up to 15 minutes, a spokeswoman for the Mumbai airport said, following several cancellations late on Tuesday.

The deluge revived memories of 2005 floods that killed more than 500 people, the majority of them in shantytown slums where more than half the city's population lives.

Unabated construction on floodplains and coastal areas, as well as stormwater drains and waterways clogged by plastic garbage have made the city increasingly vulnerable to storms.

In a message on social network Twitter, Indian Prime Minister Narendra Modi offered crisis-mitigation assistance to the government of Maharashtra, the western state whose capital Mumbai is.

More than 1,200 people have died across India, Bangladesh and Nepal in the worst floods to strike South Asia in years.