More than 50 people have been killed and many are unaccounted for in fierce storms and flooding that have hit the Bay of Bengal since the weekend.
Relatives of the dead in Andhra Pradesh will get compensation
Officials in Bangladesh believe scores of fishermen may be missing.
Indian authorities say dozens were killed and hundreds are missing in Andhra Pradesh state.
More than 140,000 have been evacuated there after rains swelled rivers and inundated villages, disrupting roads, trains and power supplies.
The weekend's rains caused the sea to rise up to 3m (10ft) in coastal areas along the Bay of Bengal.
The death toll in Andhra Pradesh has risen to 58, the commissioner for disaster management, Shashank Goel, said.
Indian Prime Minister Manmohan Singh has announced compensation of 100,000 rupees ($2,300) each to the families of those killed.
The BBC's Omer Farooq in the state capital, Hyderabad, says the state government has set up 465 relief camps in the affected districts of Khammam, East and West Godavari and Krishna.
Mr Goel said that in Khammam district alone 30,000 people were evacuated to relief camps.
About 70,000 houses in the state were flooded - more than 7,000 of them destroyed.
Some parts of the state have received record rainfall, officials say.
Helicopters have been used to rescue stranded villagers.
In Orissa state in eastern India, 11,000 people were evacuated from low-lying areas. State Revenue Minister Manmohan Samal told the BBC that more than 25,000 hectares of rice crop were destroyed by the storm.
A cyclone in Orissa in 1999 killed up to 10,000 people.
In Bangladesh, 16 fishermen are thought to have drowned when their trawlers sank in stormy weather.
Scores more are missing according to local officials and the media were reporting that anxious families were waiting along the coastlines for their relatives to return.
Bangladesh television said as many as 200 boats were initially reported missing but the government says it cannot yet confirm the figures.
A government official told the Associated Press news agency that there were not enough boats to conduct a fully fledged search.