The displaced have gathered in 450 camps, the officials said, with a total of about 1.7 million affected, along with extensive damage to infrastructure, crops and livestock.
Most deaths were caused by landslides though some followed the collapse of mud walls and drowning, another disaster management official said on condition of anonymity as he was not authorised to speak to the media.
The Indian Army said more than 80 of its personnel joined in rescue efforts, bringing to safety 334 people stranded by rising floodwaters.
In Bangladesh, the Gomti broke through an embankment late on Thursday, inundating at least 15 villages and displacing hundreds of families, officials and witnesses said.
In the capital, Dhaka, some people alleged this week that the floods were caused by the opening of dam sluice gates in India, an assertion New Delhi has rejected.
It was “not correct” that the floods were caused by water released from Tripura’s Dumbur dam on the Gomti, the foreign ministry said.
Blocked roads in several districts of Bangladesh isolated people and hampered rescue and relief efforts, officials said.
Strong currents of floodwater gushed through the districts of Feni, Moulvibazar and Noakhali where roads were inundated and ropes used to pull stranded people to safety, television videos showed.
“I have never seen such a flood in my lifetime,” said Noakhali resident Mohammad Alam.
More than 75,000 people were taken to over 1,500 shelters in the flood-hit districts, with military and border guards helping in the rescue, authorities said.