The monsoon -- which usually falls from June to September -- is crucial to the economy of the Indian sub-continent, but also causes widespread death and destruction across the region each year.
"This is going to be the worst flood in a decade," Bangladesh's Flood Forecasting and Warning Centre chief Arifuzzaman Bhuiyan told AFP.
The heavy rains have swollen two main Himalayan river systems -- the Brahmaputra and the Ganges -- that flow through India and Bangladesh.
A third of Bangladesh underwater
Bhuiyan said about a third of flood-prone Bangladesh -- a delta-nation crisscrossed by hundreds of rivers -- was underwater, and at least 1.5 million people were affected, with village homes and roads flooded.
In north-central Bangladesh, the Brahmaputra river was almost 40 centimetres (16 inches) higher than normal and threatening to burst its banks, district administrator Farook Ahmed told AFP.
Most villagers were trying to stay near their flood-damaged homes, but some 15,000 had fled severely affected areas, officials said.
With a 10-day forecast pointing to rising waters, Bhuiyan said if more rivers burst their banks some 40 percent of the nation could be flooded "in a worst-case scenario".
In the northern town of Biswambharpur, villagers said most of the houses were partly underwater after the Surma, a major river in northeast Bangladesh, burst its banks.
Farmer Abdur Rashid, 35, said he sent his wife and three children to a multi-storied village school that has been turned into a government shelter.
"My whole house has gone underwater. I have sent the rest of the family to the school, but I stayed behind to guard my properties," Rashid told AFP
Assam's Kaziranga national park
According to the bulletin released by the SDMA on Wednesday, the floods have affected 167 out of 223 camps at the Kaziranga National Park. As many as 66 animals have been killed, while 117 others have been rescued in the national park, the bulletin said.
2.1 million affected in India
In Assam, northeast India, more than 2.1 million people have been affected since mid-May.
At least 50 people have died so far -- 12 in the past week as floodwaters surged -- with tens of thousands of mostly rural residents evacuated to relief camps, officials said.
Two major challenges
Emergency services personnel wore head-to-toe bright-orange suits to protect themselves from the floods and coronavirus -- which has infected almost 17,000 people in Assam -- as they used boats to reach stranded villagers.
"We have two challenges here, one is COVID-19 and another is (the) flood," the head of a local rescue team, Abhijeet Kumar Verma, told AFP.