Both countries have asked the military to help with the severe flooding, which could worsen because rains are expected to continue over the weekend.
At least 50 people have died as floods triggered by heavy downpour cut a swatch across northeastern India and Bangladesh, leaving millions of homes underwater.
Police in Bangladesh said on Saturday monsoon rains have killed at least 25 people and unleashed the devastating floods that left more than four million people stranded.
Lightning strikes killed 21 people around the South Asian nation since Friday while the four others died in landslides triggered by the storms, police officers said.
At least 16 people have been killed in India's remote Meghalaya, the state's chief minister Conrad Sangma wrote on Twitter, after landslides and surging rivers that submerged roads.
And in India's Assam state, at least nine people died in the floods and two million saw their homes submerged in floodwaters, according to the state disaster management agency.
The Brahmaputra, one of Asia’s largest rivers, breached its mud embankments, inundating 3,000 villages and croplands in 28 of Assam’s 33 districts.
“We expect moderate to heavy rainfall in several parts of Assam till Sunday. The volume of rainfall has been unprecedented,” said Sanjay O’Neil, an official at the meteorological station in Gauhati, Assam’s capital.
Situation 'likely to deteriorate'
Several train services were cancelled in India amid incessant rains over the past five days.
In southern Assam’s Haflong town, the railway station was under water and flooded rivers deposited mud and silt along the rail tracks.
In Bangladesh, districts near the Indian border have been worst affected. Water levels in all major rivers across the country were rising, according to the flood forecasting and warning centre in capital Dhaka.
The centre said the flood situation is likely to deteriorate in the worst-hit Sunamganj and Sylhet northeastern districts and in Lalmonirhat, Kurigram, Nilphamari and Rangpur in northern Bangladesh.
Authorities suspended imminent high school graduation tests across the country, with hundreds of classrooms now being used as makeshift shelters for those whose homes have been submerged.
Flight operations at the Osmani International Airport in Sylhet have been suspended for three days as floodwaters have almost reached the runway, according to Hafiz Ahmed, the airport manager.
Last month, a pre-monsoon flash flood, triggered by an onrush of water from upstream in India’s northeastern states, hit Bangladesh’s northern and northeastern regions, destroying crops and damaging infrastructure.
Bangladesh, a nation of 160 million people, is low-lying and faces threats from climate change-related natural disasters such as floods and cyclones.
According to the UN’s Intergovernmental Panel on Climate Change, about 17 percent of people in Bangladesh would need to be relocated over the next decade or so if global warming persists at the present rate.