Residents of the Bangladeshi capital Dhaka are trying to build up defences against rising floodwaters which have already covered 40% of the city.
Slums have been inundated for days
Nearly three-quarters of the country is under water, and more than 200 people are reported to have died.
Across the whole of South Asia, more than 550 people have been killed as a result of monsoon flooding since June.
Although the Ganges and Meghna rivers have begun to recede upstream in India, forecasts predict heavy rain to come.
At least 20 million people in Bangladesh have been left homeless or stranded.
In some areas the waters have neared the highest level ever recorded.
Relief workers and volunteers jammed sandbags against cracked flood embankments in Dhaka to try to hold back the flow.
The BBC's Roland Buerk in the city says the slums on the capital's low-lying land have been inundated for days with black and stinking water from overflowing drains.
Families in Dhaka have been forced to cope on the streets
Several thousand people have gone to hospital suffering from diarrhoea.
Some people have pitched makeshift shelters on pavements after being forced out of their homes.
Our correspondent says Bangladesh is well used to flooding, but this year has been far worse than usual and the monsoon has only just begun.
Government relief workers have been handing out
food, medicines and clothes, but Bangladesh has so far refused to call for international aid, saying its own distribution efforts will be sufficient.
Millions of people are also suffering in India's north-east.
In the state of Assam, soldiers have taken to boats to hand out supplies, because road and rail links have been cut for weeks.
Officials say more than 100 people have died.
The BBC's Subir Bhaumik, who is in the state, says the air force has been airlifting supplies of fresh drinking water.
Bihar state has also been badly hit - the authorities say 225 people have died there.