The flood waters from the tributaries of the Brahmaputra and Padma rivers are expected to reach the eastern suburbs of the capital Dhaka in the next two days.
More than half a million people have been marooned in more than 30 districts of the low-lying country, officials said. Newspapers put the number of people stranded at five million.
Tens of thousands of people in neighbouring India have also been displaced from their homes or cut off in their villages as the annual South Asia monsoon drenches much of the subcontinent.
People were facing shortages of food, drinking water and medicine at relief camps, while a lack of boats has hampered rescue efforts, officials said.
A local official in northern Bogra district said he had received frantic calls from people in flooded villages.
"Please send us a boat," commissioner Furti Begum quoted one desperate villager as telling her in a mobile phone call from the village of Kajlarchar, 50 km (30 miles) from the Bogra town.
"Probably this is my last call as the mobile is running out of battery charge," the man named Soleman said.
Begum said thousands of people have been perching on the roofs of their homes for over a week, but evacuation was difficult because of a lack of boats.
On Tuesday, the entire Sirajganj town with about 150,000 people was under waist-high water, witnesses said. Boats were plying the town, selling dry food rations to residents.
Over a dozen rivers, including the Brahmaputra, Jamuna, Padma and Meghna were flowing more than one metre above their danger levels, and are still rising, weather officials said.
Meanwhile thousands of villagers near the Bangladeshi city of Chittagong flocked to see the rare sight of a beached whale on Monday.
The whale carcass washed up on a beach near the port city and Mohammad Faruk, a fisheries department official said: "Local fishermen initially thought it was wreckage from a grounded ship."
It was not clear what species the whale belonged to or how it died.
The tail and fins of the whale, meanwhile, appeared to be mutilated, private television channel ATN Bangla said.
Migrating whales are sometimes sighted in the Bay of Bengal off Bangladesh's southern coast, but rarely come near shore, experts and witnesses say.
|Whales are rarely seen near the shore in Bangladesh [Reuters]|