Protesters at camps in West Bengal have complained of a lack of food. People have also been clamouring for plastic sheets to build temporary shelter.
At least 400 people have died in the flooding in West Bengal and more than 15 million people left homeless.
Officials say 200 people are missing in what are being described as the worst floods in the region in more than 30 years.
There has been rioting in relief camps set up for tens of thousands of people whose homes have been inundated.
Reports say more bad weather and more waves of floodwater from dangerously full dams are expected.
Food riots
However, West Bengal state authorities have complained that rescue work has been severely hampered by theft and looting. Some relief officials have been beaten up.
Protesters at camps in West Bengal have complained of a lack of food. People have also been clamouring for plastic sheets to build temporary shelter.
Murshidabad is the worst affected area. Seven villages were totally washed away.
Opposition parties have accused the left-wing West Bengal state government of mismanaging relief funds.
"It is natural that people would try to snatch food if they have had to go hungry for days," Congress Party leader Paresh Bal said.
Helicopters have been airlifting food and water supplies to some of the millions of people still stranded.
Rescue attempts
The army has deployed several battalions to conduct relief and rescue operations but have been hampered by shortages of speedboats.
The floods have swept away roads and railway tracks in many places, cutting off the flooded areas from the rest of the state and further hampering rescue efforts.
In the neighbouring state of Bihar, where some areas have been flooded, swollen rivers swept away a stretch of railway track.
In Bangladesh, rains washed out mud embankments, swamped 50 villages and marooned up to 250,000 people in the north according to relief officials in the country.
The army has been called to help evacuate thousands marooned in five affected districts.