Millions of people have been stranded while emergency workers have struggled to reach those affected.
Forecasters are warning that the flooding is expected to get worse over the next few days.
Some Bangladesh government officials have described the recent flooding as the country's worst since 2004.
Unrelenting rains over the last week have inundated vast swathes of the country's north-east region, exacerbated by run-off from heavy downpours across mountains in neighbouring India.
Schools have been converted into makeshift shelters, while troops have been deployed to evacuate households cut off from neighbouring communities as a result of rising waters.
"The whole village went under water by early Friday and we all got stranded," Lokman, whose family lives in Companiganj village in Bangladesh, told AFP news agency.
"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.
Sylhet, in northeast Bangladesh, has seen villagers wade through streets that were flooded up to their knees.
In Assam state in neighbouring India, 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.
"Our house is submerged in water. I've never seen such huge floods in my life," Husna Begum, a resident of Udiana village in Assam, told the BBC.
The 28-year-old has been living in a rickety plastic tent with her children since Thursday. "There is no drinking water in the camp here. My son has a fever, but I am unable to take him to the doctor," she said.
Ronju Chaudhary, who lives in the same village, described the scale of the flooding. "We are surrounded by water on all sides. There's water inside our homes too," he said.