Two were electrocuted at Sonarpur and Canning in South 24 Parganas district after an overhead wire snapped and fell on them during heavy rain.
Four people including three women were killed and three sustained serious injuries in a house collapse in West Midnapore and South 24 Parganas districts, reports said.
Anita Adhikary, 35, was killed and her 12-year-old daughter Pinki was injured when their mud house caved in at Nodakhali village in South 24-Parganas.
Atmajan Bibi, 45, was killed and her husband and daughter were seriously injured when their thatched hut collapsed. Chhabi Manna, 35, was also killed in the same district when the parapet under which she took cover during the rain gave away. Another elderly person in Danton in West Midnapore district was found dead under the debris of his collapsed home.
Reports said over 500 dwellings were damaged, mostly in South 24 Parganas district after freak winds with a velocity of 70 km per hour lashed two villages.
State Inspector General Banibrata Basu confirmed the deaths of six people.
Many roads and low-lying areas in north, south and central parts of the city have been inundated. Rains have severely affected the train services in both the Eastern and South Eastern Railways in the region.
Several flights to and from Kolkata were delayed and some flights were diverted because of inclement weather, an airport official said. The meteorological office here said the stormy weather and heavy spell of rain would continue for the next 24 hours as the depression formed over the west-central Bay of Bengal would take another couple of days to weaken.