The cyclone is expected to cross Khulna coast around Saturday midnight
Four people have died and tens of thousands spent a night huddled in storm shelters as Cyclone Bulbul smashed into Indian coasts with fierce gales and torrential rains.
The cyclone packed winds of up to 120kmph when it hit late Saturday, closing ports and airports in both countries.
Three people were killed in India's West Bengal state, two after uprooted trees fell on their homes and another after being struck by the falling branches of a tree in Kolkata. A fourth person died in a wall collapse in nearby Odisha state, officials said Sunday.
In Bangladesh, four more were killed by falling trees and several were injured. The cyclone also damaged some 4,000 mostly mud and tin-built houses, Bangladesh's Disaster Management secretary Shah Kamal told AFP.
In coastal Khulna, the worst-hit district in Bangladesh, trees swayed violently and were ripped from the ground in the fierce storm, blocking roads and hampering access to the area.
Some low-lying parts of the district were flooded, Disaster Management Minister Enamur Rahman told AFP.
Authorities said the cyclone was weakening as it moved inland.
"It has turned into a deep depression, causing heavy rainfall," Bangladesh weather bureau Deputy Chief Ayesha Khatun told AFP.
Bulbul hit the coast at the Sundarbans, the world's largest mangrove forest which straddles Bangladesh and India, and is home to endangered species including the Bengal tigers and the Irrawaddy dolphins.
The mangroves shielded the coast from the storm's full impact, Khatun said.
Trail of destruction
Some 2.1 million people across Bangladesh were relocated to cyclone shelters.
Troops were sent to coastal districts while tens of thousands of volunteers went door-to-door and used loudspeakers to urge people to evacuate their villages.
In India, nearly 120,000 people who were evacuated started to return home as the cyclone weakened, authorities said.
"The storm has left a trail of destruction as it's crossed the coastline of West Bengal," the state's Urban Development Minister Firhad Hakim said.
"Trees were uprooted, thatched and corrugated roofs of many houses were blown away."
Bangladesh's low-lying coast, home to 30 million people, and India's east are regularly battered by cyclones.
Hundreds of thousands of people living around the Bay of Bengal have been killed in cyclones in recent decades.
While the frequency and intensity of the storms have increased, partly due to climate change, the death tolls have come down because of faster evacuations and the building of thousands of coastal shelters.
Cyclone Fani was the most powerful storm to hit the area in years when it struck in May, killing 12 people.
Cyclone Bulbul weakens in Bangladesh
The cyclonic storm Bulbul over Khulna and adjoining northwestern parts of Bangladesh weakened further into a deep depression and moved slowly northeastwards.
It was over Bagerhat, Barisal and Patuakhali regions at 6am on Sunday, according to the Met office.
Bulbul is likely to move in a northeasterly direction further and weaken gradually by giving precipitation.
The powerful storm completed crossing West Bengal-Khulna coast near Sundarbans around 5am on Sunday.
At a special weather bulletin on Sunday morning, the Met office asked maritime ports of Mongla and Payra to lower great danger signal number 10, and Chittagong to lower great danger signal number nine. Instead, the ports are advised to hoist local cautionary signal number three.
Besides, maritime port of Cox's Bazar has been advised to lower local warning signal number four, and hoist local cautionary signal number three, the bulletin said.
Under the influence of the deep depression, the coastal districts of Khulna, Satkhira, Chittagong, Noakhali, Lakshmipur, Feni, Chandpur, Barguna, Patuakhali, Barisal, Bhola, Pirojpur, Jhalakathi, Bagerhat, Faridpur, Madaripur, Comilla, Dhaka, Sylhet, and Mymensingh are likely to experience wind of 50-60kph in gusts with heavy to very heavy falls during the passage of the deep depression.