The strongest cyclone in decades landed on Bangladesh and eastern India today, sending water surging inland and leaving a trail of destruction as the death toll rose to at least nine.

High winds and torrid rains pounded coastal villages and cities, bringing down power lines, uprooting trees and inundating homes.

"The situation is more worrying than the coronavirus pandemic. We don't know how to handle it," India's West Bengal state leader Mamata Banerjee told reporters.

"Almost everything is destroyed in the coastal villages of the state... It uprooted many trees and inundated many roads in (the capital city) Kolkata."

Authorities had scrambled to evacuate more than three million people from low-lying areas, but the task was complicated by the need to prevent the spread of coronavirus.

In Bangladesh officials confirmed six deaths including a five-year-old boy and a 75-year-old man, both hit by falling trees, and a cyclone emergency volunteer who drowned.

Three more died after being hit by uprooted trees in West Bengal, the state's disaster management minister Javed Khan told AFP.

Two other fatalities were reported by Indian media, including an infant crushed when the mud wall of the family's hut collapsed in heavy rain in Odisha state. AFP could not verify the deaths.

Heavy rains and winds up to 113km/ph lashed Kolkata - home to some 14.7 million people - plunging some of the historic city into darkness as power and communication lines were knocked out.

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Amphan is the first "super cyclone" to form over the Bay of Bengal since 1999, and packed winds gusting up to 185km/ph.

It brought a storm surge - a wall of ocean water that is often one of the main killers in major weather systems - that roared inland for several kilometres, media reports said.

In southwestern Bangladesh, a five-feet-high storm surge broke an embankment and swamped a large area of farmland, a local police officer told AFP.

Bangladesh officials were particularly concerned about the damage to the Sunderbans, a UNESCO world heritage site famed for its mangrove forest and tiger population, which they said bore the brunt of the cyclone.

"We still haven't got the actual picture of the damage. We are particularly concerned over some wild animals. They can be washed away during storm surge in high tide," forest chief Moyeen Uddin Khan told AFP.

Bangladesh's low-lying coast, home to 30 million people, and India's east are regularly battered by cyclones that have claimed the lives of hundreds of thousands of people in recent decades.

The 1999 super cyclone left nearly 10,000 dead in Odisha, eight years after a typhoon, tornadoes and flooding killed 139,000 in Bangladesh. In 1970, half a million perished.

While the frequency and intensity of storms have increased - blamed partly on climate change - casualties have fallen thanks to faster evacuations, better technology and more shelters.

Bangladesh authorities had feared Amphan will be the most powerful storm front since Cyclone Sidr killed about 3,500 people in 2007.

Enamur Rahman, Bangladesh's junior minister for disaster management, told AFP 2.4 million people and over half a million livestock were brought to shelters.

India evacuated more than 650,000 in West Bengal and Odisha.