A pedestrian makes his way under heavy rain in Khulna, Bangladesh, on Sunday. AFP

Eight people died and more than two million others spent a night huddled in storm shelters as Cyclone Bulbul smashed into the coasts of India and Bangladesh with fierce gales and torrential rains, officials said on Sunday.

The cyclone packed winds of up to 120 kilometres (75 miles) per hour when it hit late Saturday, closing ports and airports in both countries.

Bangladesh evacuates 100,000 as Cyclone Bulbul approaches

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.

In Bangladesh, four more were killed by falling trees and at least 20 people were injured. The cyclone also damaged some 4,000 mostly mud and tin-built houses, Bangladesh's disaster management secretary Shah Kamal told AFP.

Villagers walk on their way to enter a relief centre as Cyclone Bulbul is approaching in Indian state of West Bengal. 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 the media.

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 the meida.

Women look through a window as Cyclone Bulbul is approaching, in Dakop, Khulna, Bangladesh. AFP

According to US-based AccuWeather Inc., Bulbul strengthened from a deep depression into a tropical cyclone on Thursday morning, and by Friday afternoon had strengthened into a severe cyclone. Bulbul was the equivalent of a Category 1 or 2 hurricane in the Atlantic, it said.

Rahman said the government suspended weekend leave for government officials in 13 coastal districts on Saturday.

On Saturday, volunteers used loudspeakers to ask people to move to shelters in Chittagong and other regions, according to the Disaster Management Ministry. In the Cox's Bazar coastal district, tourists were alerted to stay in their hotels, while a few hundred visitors were stuck on Saint Martins Island.

Authorities suspended all activities in the country's main seaports, including in Chittagong, which handles almost 80 per cent of Bangladesh's exports and imports. All vessels and fishing boats were told to stop operating.

Villagers on their way to enter a relief centre in Bakkhali near Namkhana in Indian state of West Bengal. AFP

Local authorities ordered school buildings and mosques to be used as shelters in addition to dedicated cyclone shelters — raised concrete buildings that have been built over the past decades.

Bangladesh, a nation of 160 million people, has a history of violent cyclones. But disaster preparedness programs in recent decades have upgraded the country's capacity to deal with natural disasters, resulting in fewer casualties.