The rural districts of Gaibandha, Lalmonirhat, Rangpur, Jamalpur, Bogra, Nilphamari, Kurigram and Sirajganj have been inundated by the surging waters in the past two days, according to the Flood Forecasting and Warning Centre.
Rivers in the Brahammaputra-Jamuna and the Ganges-Padma-Meghna basins were flowing above the danger level and were likely to rise more, the centre said in a statement on Friday.
About 500,000 people are stranded in those districts, including 200,000 in Rangpur and Sirajganj alone, the Daily Star newspaper reported.
Two boys, aged four and five, drowned on Thursday in Gaibandha, 190km north of the capital, Dhaka, a district administration official, Rafiqul Islam, said.
A five-year-old boy drowned the same day in Jamalpur, the Janakantha daily reported.
Islam said villagers in Gaibandha district were suffering because of a lack of drinking water, and that dozens of children were suffering from water-borne diseases.
"We are monitoring the situation and trying to ferry dry foodstuffs and medicine to the victims," he said.
"We are monitoring the situation and trying to ferry dry foodstuffs and medicine to the victims"
District administration official
In Gaibandha, the raging waters washed away thousands of homes including 1200 mud and straw huts, leaving about 15,000 families homeless, the Janakantha said.
The swirling floodwaters also destroyed part of a highway in the district.
Low-lying areas around Dhaka were also submerged and many residents in the capital's suburbs relied on small boats to get around.
Seasonal floods are common in this South Asian delta nation of 140 million people. Last year, about 800 people were killed by monsoon floods in Bangladesh.