Monsoon storms in Bangladesh and India have killed at least 41 people and unleashed devastating floods that left millions of others stranded, officials said on Saturday.

Floods are a regular menace to millions of people in low-lying Bangladesh, but experts say climate change is increasing their frequency, ferocity and unpredictability.

Relentless downpours over the past week have inundated vast stretches of Bangladesh's northeast, with troops deployed to evacuate households cut off from neighbouring communities.

Schools have been turned into relief shelters to house entire villages inundated in a matter of hours by rivers that suddenly burst their banks.

“The whole village went under water by early Friday and we all got stranded,” said Lokman, whose family lives in Companiganj village.

“After waiting a whole day on the roof of our home, a neighbour rescued us with a makeshift boat. My mother said she has never seen such floods in her entire life,” the 23-year-old added.

Asma Akter, another woman rescued from the rising waters, said her family had not been able to eat for two days.

“The water rose so quickly we couldn't bring any of our things,” she said.

“And how can you cook anything when everything is underwater?”

Lightning triggered by the storms has killed at least 21 people around the South Asian nation since Friday afternoon, police officials told AFP.

Among them were three children aged between 12 and 14 who were struck by lightning on Friday in the rural town of Nandail, said local police chief Mizanur Rahman.

Another four people died when landslides hit their hillside homes in the port city of Chittagong, police inspector Nurul Islam told AFP.

At least 16 people have been killed since Thursday in India's remote Meghalaya, the state's chief minister Conrad Sangma wrote on Twitter, after landslides and surging rivers that submerged roads.

Next door in Assam state, more than 1.8 million people have been affected by floods after five days of incessant downpours.

Assam chief minister Himanta Biswa Sarma told reporters he had instructed district officials to provide “all necessary help and relief” to those caught in the flooding.

'The situation is bad'

Flooding in Bangladesh worsened on Saturday morning after a temporary reprieve from the rains the previous afternoon, Sylhet region chief government administrator Mosharraf Hossain told AFP.

“The situation is bad. More than four million people have been stranded by flood water,” Hossain said, adding that nearly the entire region was without electricity.

The flooding forced Bangladesh's third-largest international airport in Sylhet to shut down on Friday.

Around the regional capital, residents waded through waist-deep water along roads next to partially submerged stuck vehicles.

Forecasters said the floods were set to worsen over the next two days with heavy rains in Bangladesh and upstream in India's northeast.

Before this week's rains, the Sylhet region was still recovering from its worst floods in nearly two decades late last month, when at least 10 people were killed and four million others were affected.