Six people, including five children, were killed after a building collapsed in Mumbai, officials said on Monday, as monsoon rains lashed India's financial capital, flooding roads and forcing the closure of schools.

A dilapidated residential building collapsed on Sunday in the eastern part of the megacity, trapping residents beneath the debris, Mumbai Mayor Ritu Tawde said in a statement.

The fatalities came as torrential rain brought parts of the city to a standstill, with the India Meteorological Department recording more than 200 millimetres (7.8 inches) of rainfall in the 24 hours to Monday.

Hundreds of millions of people across India rely on the annual monsoon to bring the rainfall that sustains agriculture and industry.

However, climate change is altering weather patterns and making the world's most populous country increasingly hotter. This year's El Niño weather phenomenon has also prompted warnings of below-average rainfall.

The weather office issued a red alert for Mumbai on Monday, forecasting continued heavy rain and strong, gusty winds.

With roads submerged, the city authorities declared a holiday for all schools and colleges on Monday.

Mayor Tawde urged residents to remain indoors where possible, warning of the risk of falling trees and branches due to the strong winds.

The downpours followed weeks of sweltering heat, during which authorities imposed restrictions on water use last month and reduced supplies to swimming pools and construction sites.

The city of more than 20 million people is also facing growing concerns over pressure on its water resources from the expansion of data centre infrastructure, whose substantial cooling requirements could place further strain on supplies.