But the rescue in driving rains was proving hazardous, with a boat taking 50 people to safety in India's eastern Bihar state overturning and a helicopter crashing trying to reach stranded students of a Bihar medical college.
Some 35 people were swept away feared drowned when the boat sank in the Bagmati river, 70 kilometres (43 miles) north of Bihar state capital Patna. There were no casualties when the helicopter crashed near the town of Darbhanga, police and witnesses said.
The total number of dead and missing in India now stands at 160, while a burst dam which swamped villages in Bangladesh pushed the toll there to 105, according to an AFP tally based on reports and official figures.
In Nepal, the head of the Natural Disaster and Floods Division of the Home Ministry, Durga Pokharel, on Thursday put the toll at 77 dead and nine missing.
Authorities in India's eastern Bihar state reported more than nine million people had been affected by flooding, opening up a new front for police, troops and civil authorities already battling to prevent a human catastrophe in low-lying areas of east and northeast India, Bangladesh and Nepal.
A further five million have been hit in India's northeastern Assam state and four million in Bangladesh, according to officials.
Across the region, tens of thousands of people have taken shelter on raised bamboo stilts and on mud embankments, some even on rooftops of their mud-and-straw huts waiting to be rescued, officials said.
"We have moved all our resources for rescue and relief and more army support has been made available," K.A.H. Subramanian, Bihar state chief secretary, told a press conference late Wednesday.
"A total of 9.436 million people in 16 northern districts of (Bihar) have been affected," said Subramanian, adding the floods were "the worst in 17 years".
Subramanian said around 3,652 villages had been affected in Bihar, of which 1,170 had been completely cut off or were inundated. Four entire districts were completely submerged.
Ten small and large helicopters and 1,432 boats had been put into service for rescue and relief works, the state disaster management cell said.
The death toll in neighbouring Assam climbed after two people died when a boat capsized, while nine workers were buried when landslides wiped away their homes overnight, officials said.
"The floods this time are really very serious. We don't have anything left, not even food," said Narayan Gharphulia, a villager in the worst-hit Nalbari district in western Assam, said by telephone.
"Unless we get urgent food supplies, we are doomed."
Assam State Chief Minister Tarun Gogoi told AFP that the army was out in full force to help those affected.
"So far we have rescued about 3,000 people, besides helping villagers with food and medical facilities," an army spokesman said.
In northwest Bangladesh, five people drowned and 60 others were missing after a dam holding back floodwaters was sabotaged, unleashing a torrent which swept through nearby villages, a report said Thursday.
The deaths of four children and a 58-year-old woman had been confirmed while a search was underway for 60 others swept away by the flooded Jamuna river, the English-language Daily Star said.
In Nepal, where 28 of the country's 75 districts have been affected by floods, the monsoon rains began easing on Wednesday, but relief operations were still in full swing, said Home Minister Purna Bahadur Khadka.
"We are doing necessary relief work on a war-footing to help the flood and mudslide victims," Khadka said told AFP.