Worst affected is the northern Indian state of Bihar, where some 1.9 million people have fled their homes due to rising waters, a state government release said.
Television channels showed roads and railway lines in Bihar submerged, with people wading through chest-high, brown, churning waters, carrying their belongings on their heads.
An impoverished agrarian province with rickety infrastructure and poor healthcare services, Bihar has a history of flooding in its northern areas that border Nepal.
Flood waters in the northeastern Indian state of Assam rose overnight with the Brahmaputra river, which flows down from the Himalayas into Bangladesh, and its tributaries still in spate.
More than 1.7 million people in Assam have been displaced by the floods, authorities said, and most of the Kaziranga National Park, home to the rare one-horned rhino, was also under water.
"The flood situation has turned very critical with 31 of the 32 districts affected," Assam Chief Minister Sarbananda Sonowal told reporters. "We are working on a war footing to deal with the flood situation."
Known for its tea industry, Assam is often inundated by seasonal flooding, and state and federal governments have spent millions of rupees on flood control.
India's weather office on Monday forecast widespread rains across Assam and Bihar for the next two days.
In neighboring Nepal, 64 people were killed and 31 were missing, with around a third of all districts hit by heavy rains, authorities said. Many of the deaths were caused by landslides that swept away houses.
In southeast Nepal, water levels on the Kosi river, which flows into Bihar, had receded, an district official said.
In 2008, the Kosi broke its banks and changed course, inundating huge tracts of land and killing 500 people.
“Our analysis is that the danger is over now that the water level has come down,” Chiranjibi Giri, assistant district administrator of Sunsari district, told Reuters.
The annual monsoon season, which brings the most rain across south Asia, also hit Bangladesh hard, forcing an estimated 190,000 people out of their homes, government officials said.
In Cox's Bazar district, shelter to some 700,000 Rohingya refugees who fled violence in neighboring Myanmar, more than 100,000 people have been displaced.Since early July, flooding and landslides have damaged thousands of shelters at the refugee camps, killing two people, including a child, Human Rights Watch said in a release last week.