Bangladeshi authorities were also searching for other cases of bird deaths.
No human cases have been reported in either Bangladesh or India since the latest outbreak of bird flu was first discovered earlier this week.
But nearly 56,000 birds have died from the disease in eastern India, where authorities have begun slaughtering another 400,000 animals, most of them chickens.
In Bangladesh, officials say about 20 birds have died and another 1,700 have been slaughtered.
Bangladeshi authorities say the outbreak in that country, which has so far been limited to a single poultry farm, is the H5N1 strain of the disease.
Bird flu was first detected in Bangladesh in February 2007 at a poultry farm near Dhaka, the capital.
Since then, authorities have slaughtered more than 300,000 chickens - including 19,000 killed during another outbreak earlier this month - at about 90 farms across the country.
Nearly 360,000 eggs have also been destroyed.
Tests under way
In India, where the outbreak is more widespread, authorities say they are still conducting tests to determine what strain of bird flu killed the animals.
The outbreaks are in adjacent areas of the neighbouring countries.
While bird flu seemed to be the obvious culprit in the new deaths in West Bengal, Anisur Rahman, the state's animal husbandry minister, cautioned that the symptoms indicated Newcastle disease, known locally as Ranikhet, a fatal respiratory virus that is not known to attack humans.
Health workers are also going door to door, looking for people with high fevers or breathing trouble, he said.