More than 1 million people have been marooned in Nepal, Bangladesh and India and hundreds of thousands have fled their homes for higher ground.
Indian officials said floods and mudslides killed 16 more people in the country's northeast, raising the death toll in the country to 93.
Nepal reported at least 117 deaths over the past month.
Rains caused the Brahmaputra River, which flows through Tibet, India and Bangladesh, to burst its banks in India's Assam state late last month, inundating large swathes of the state, triggering mudslides and displacing about 3.6 million people, officials said.
Vast tracts are still underwater, with 26 of the state’s 33 districts badly affected.
Authorities rescued about 4,000 people trapped by the surging flood waters in various parts of Assam, said M.S. Mannivanan, chief of the state Disaster Management Authority. About 36,000 people whose homes were destroyed or submerged have taken shelter in nearly 300 government-run relief camps, he said.
The floods also inundated most of India’s Kaziranga National Park, home to an estimated 2,500 rare one-horned rhinos, authorities said.
In the eastern state of Bihar, at least nine rivers swollen by heavy downpours in Nepal rose beyond their danger levels and inundated many villages. One of them, the Gandak River, swept away the connecting roads of a newly built multimillion dollar bridge in Bihar’s Gopalganj district, disrupting transportation in the area.
The Meteorological Center in the state capital, Patna, forecast heavy rain over the next 48 hours.
Nepal’s Home Ministry said 117 people have died in the Himalayan nation in monsoon-related incidents. It said the rains triggered landslides in mountainous areas and flooding in the southern plains. At least 47 people were reported missing and 126 have been injured in the past month, it said.