The death toll was well above 2,000 on Friday with 16 more deaths reported in Bangladesh, 19 in India's Bihar state and three more in Nepal.
Monsoon rains have halted across much of the massive Himalayan flood plain from southern Nepal to the eastern delta nation of Bangladesh, with the focus now on combating a host of water-borne diseases, health officials said.
At Bangladesh's biggest diarrhoea hospital in the capital Dhaka, doctors like Alejandro Cravioto were working around the clock amid hundreds of extra beds under tents to help flood victims.
"It's like a war-zone situation," he said, as medical staff patrolled the tents with megaphones, urging patients to take their medication and stay hydrated.
"Some patients are very ill but the treatment is extremely effective," said Cravioto, the hospital's executive director.
Thousands of villages remained under water, threatened by disease, while millions were still displaced in India and Bangladesh and desperate for relief aid.
"There are hundreds and thousands of internally displaced people camping on embankments and roads where the most urgent needs are for food, safe drinking water, sanitation facilities and shelter," the UN children's agency UNICEF said in a statement.
Several countries and international agencies have pledged assistance and money to help victims, including the European Union which has put up an initial four million euros (5.5 million dollars).
Saudi Arabia's King Abdullah ordered emergency supplies to be rushed to flood-hit Bangladesh, the official SPA news agency reported Thursday night, adding that 50 million dollars (37 million euros) was being sent to cover urgent needs in the disaster zone.
UNICEF is working with officials in Bihar, hit by the heaviest flooding in 30 years, to conduct medical surveillance and inoculate children against disease, particularly measles.
"The situation in Bihar is the most serious and continues to look grim," the agency said, noting that nearly 132,000 houses have been destroyed and nearly half a million damaged.
The Indian government announced emergency aid for flood victims, with Bihar, where at least 1.1 million hectares (2.7 million acres) of farmland have been inundated and 14 million people affected, scheduled to get 37 million dollars.
Early estimates of the monsoon's cost to India stand at about 320 million dollars, though the figure is expected to rise.
The UN agency said that in Bangladesh 7,600 of more than 8,600 primary schools are closed and 23,000 cases of diarrhoea have been reported. The government there has urged citizens and foreign donors to help feed nine million displaced people.
The annual monsoon rains that soak the subcontinent from June through September are crucial for the farm-dependent economies in the region, but also wreak death and destruction.
India's home ministry reported 1,550 deaths across the country from this year's monsoon up to Thursday afternoon.
The figures do not include scores of people still missing from numerous boating accidents.
In Bangladesh the toll reached 362 after more deaths overnight, the food and disaster management ministry said.
In Nepal, the death toll rose to 99 after three people were swept away in a river in the south-west, the home ministry said, although the flooded lowlands had not received any rains for the past two days.
UNICEF reported that many of the 330,000 people displaced were returning to villages from relief camps.