At least 72 people have died as Cyclone Amphan ripped through densely populated coastal areas of eastern India and Bangladesh.

Amphan was one of the worst storms over the Bay of Bengal in years.

The powerful cyclone destroyed thousands of homes, uprooted trees and downed power cables, leaving authorities struggling to mount relief efforts amid the coronavirus crisis.

Tidal surges swallowed embankments and bridges, and left villages without access to fresh water, electricity and communications, officials said.

Cyclone Amphan has brought destruction to large parts of India and Bangladesh. Credit: AP

Amphan made landfall in India's coastal state area of West Bengal on Wednesday and has had an adverse effect on the weather in various parts of the country.

“The impact of Amphan is worse than the coronavirus pandemic,” First Minister of West Bengal Mamta Banerjee said.

"Thousands of mud huts have been levelled, trees uprooted, roads washed away and crops destroyed.

"It is a catastrophe...

"Communications are disrupted," Ms Banerjee said.

Cyclone Amphan over the Bay of Bengal in India Credit: NASA Worldview, Earth Observing System Data and Information System (EOSDIS) via AP

With rains continuing, she said the hardest hits areas were not immediately accessible.

Residents in many parts of Kolkata, the capital of the hard-hit West Bengal state, woke to find streets flooded with several feet of water.

“Our windows rattled, the house shook, trees have collapsed,” said a Kolkata resident.

The city's airport remains shut after flooding caused damage.

Kolkata and many of the surrounding districts faced power outages, although supplies in many areas have been restored.

As Amphan continues to wreak havoc in neighbouring Bangladesh, more than five million people have been left without electricity.

"The cyclone made landfall on the Digha coast in India yesterday afternoon and then moved towards Bangladesh through the south-western part," Shamsuddin Ahmed, director of Bangladesh Meteorological Department said.