In India, Northern Uttar Pradesh and Bihar states and northeastern Assam were among the worst affected.
As many as 10 million people have been displaced in Bihar alone.
Another 5.5 million were displaced in Assam, with a further 1.4 million displaced in Uttar Pradesh, officials have said, with heavy rains expected to continue.
Health workers and aid groups in Assam began to treat and feed the displaced with limited medicines and supplies.
Elsewhere, villagers were getting desperate and hungry.
"Our family survived for a week on buffalo milk but now the animal has stopped producing milk as it has gone without food for days," said Meghu Yadav, a villager in the Samastipur district of Bihar state.
Elsewhere in Bihar angry protests by people forced from their homes erupted after one villager was killed and more than 20 injured in clashes with police, officials and witnesses said.
The violence flared in the Madhubani district late on Friday when police tried to move the displaced from elevated train tracks where they had taken refuge, in order to dig a ditch and drain floodwaters from a nearby village.
Police opened fire, killing one villager, witnesses said.
The NDTV news channel reported officers had been pelted with stonesMore deaths
In Bangladesh, at least 16 people, including six children, drowned overnight taking the country's death toll to at least 81, an official at the government's flood monitoring agency has said.
"We have been virtually starving for several days but there seems to be no one to come to help us," said Majeda Begum, perched on the roof of her house in Manikganj district with her five-year-old granddaughter.
|Displaced Indian villagers have been taking|
refuge in schools [AFP]
The floods have spread to 41 of Bangladesh's 64 districts.
In the Shibalaya area of Manikganj, about 170 km north of the capital Dhaka, reporters saw villagers offering prayers on boats as mosques had been flooded.
Parts of Dhaka are under water and more areas might flood in the next few days.
In Nepal, the UN has said that rains over the last few weeks had triggered floods and landslides in both the west and east that have killed 84 and displaced 270,000 people.
The Nepalese army and rafting companies - used to taking tourists - have joined rescue operations.
Hospitals in eastern India were packed on Saturday with people suffering from diarrhoea, dysentery and fever.
On Friday, Unicef had said that the scale of the disaster posed an "unprecedented challenge" for aid workers.
"The victims are left to survive on their own," said an aid worker with an Indian voluntary agency, supervising relief work in Assam.