Incessant downpours for more than a week made the Brahmaputra and other rivers burst their banks across Assam and Bihar states.
Experts say the annual floods are getting worse because of climate change. Authorities released water at one dam, fearing the walls would collapse.
Tens of thousands of people are stuck in villages cut off by the floods and the Assam governments said more than 400,000 had been moved to higher ground.
Sixteen-year-old Anuwara Khatun said she and her family have spent nearly a week on the roof of their home at Ghasbari in the state’s Morigaon district.
“The water level has been rising for five days now,” she told the AFP news agency by telephone from her stricken village on the banks of the Brahmaputra.
“A lot of families are stuck on their roofs. There is a shortage of essential supplies so we only eat once a day. There is no hygiene here.”
Santosh Mandal moved his family to a sandbank in Bihar’s Supaul district after his village was flooded.
“There is no clean water to drink, food to eat and the children are crying for milk. We are praying for help because the government has yet to send relief,” Mandal said.
The Bihar government has sent rescue boats to get people to safety but these are concentrated in the worst-hit districts.
The Bihar government opened up the Valmiki Gandak dam, warning people in nearby villages to move away, after 160mm (six inches) of rain fell in 24 hours.
The floods have also threatened the Kaziranga National Park in Assam, a UNESCO World Heritage-listed reserve that is home to the largest concentration of rare one-horned rhinoceroses.
About 70 percent of the 430sq km (166sq mile) park is underwater, threatening its rhinos as well as elephants and wild boar.
Himanta Biswa Sarma, Assam’s chief minister, on Monday made an “urgent appeal” for traffic to avoid a key highway through the reserve.
He said animals that seek shelter on the highway were now at risk.