At least 1.6 million have been made homeless in West Bengal, according to authorities.
Schools and colleges in the affected districts have been ordered shut to house displaced people.
In neighbouring Orissa, nearly one million people had been cut off after four rivers overflowed, Manmohan Samal, the disaster management minister, said.
Medical teams have been sent to affected areas and air force helicopters were due to drop food packets.
The heavy rains have also caused flooding in Assam state, and in the northeastern region of Arunachal Pradesh 19 people died over the weekend due to mudslides triggered by a heavy downpour.
More than 350,000 people had taken shelter in government camps in Assam to escape from rising waters, the government said earlier
this week, before flood waters started receding on Wednesday.
Every year the monsoon rains cause the Brahmaputra river to flood, submerging paddy fields, washing away villages, drowning livestock and killing people in Assam.
In 2004, at least 200 people died and more than 12 million were displaced by floods.