Local media said two children had died in the badly-hit district of Patuakhali, in southern Bangladesh, which hit the country on November 15.
"The sanitary situation is awful, we lack fresh water," a Bangladeshi food and emergency ministry spokesman said.
The cyclone, which was called "a national calamity" by Fakhruddin Ahmed, the country's interim government head, destroyed over 270,000 homes affecting up to 4 million people. Bangladesh's leader added, "The destruction of houses, roads, trees and crops by the hurricane is unimaginable."
The Bangladeshi Red Crescent Society earlier said that the final death toll could reach 10,000, as official statistics had failed to take into account victims on coastal islands and in isolated areas.
Relief workers are struggling to distribute drinking water and food to affected areas and are reported to be running out of supplies.
Rescue and relief missions have been sent to about 90% of the affected areas, while the rest of the territory ravaged by the cyclone is expected to be reached Thursday.
In a statement on the crisis, United Nations Secretary-General Ban Ki-moon pledged the full support of the organization.
"The UN is ready and willing to help them in any way possible," he said. "We have made clear that several million dollars are available from the Central Emergency Response Fund."
So far around $140 million in international aid has been pledged with the European Union promising around $10 million and the American Red Cross about $1 million.
The U.K., Germany, France, Japan, Italy, the Philippines, and the Netherlands have also promised to assist the stricken south Asian country.
This is the worst storm to hit Bangladesh since 1991, when at least 139,000 people were killed along its coastline. In 1970, a cyclone claimed around half a million lives in the country.
