By Subir Bhaumik
BBC News, Calcutta
Tests on dead birds from Dinhata, less than a two-hour drive from Calcutta, have tested positive for the disease.
Nine of the state's 19 districts have been already hit by the flu. Officials say more than 2m birds would be culled.
The H5N1 strain of bird flu is regarded as highly pathogenic and can also cause disease and death in humans.
Health experts have warned that the outbreak could get out of control.
No cases of human infection have still been reported though a member of the culling team has been admitted to hospital with respiratory disorder and fever.
State animal husbandry minister Anisur Rehman said the government had a "long way to go" in culling the targeted two million birds.
Only a third of the target has been achieved - barely 700,000 birds have been culled in the last 10 days.
"More culling teams are needed in all the affected districts but these are things that cannot be hurried. The men in the culling teams have to be quarantined first before they can be asked to start the operations," Mr Rehman said.
In most of the districts , the villagers were resisting culling of their backyard poultry.
"Poultry is a major source of income for the poor villagers. It is not unusual for them to resist culling. So we have to persuade them rather than force them," said Manasa Hansda, a senior official of Birbhum, one of the worst-hit districts said.
The problem is made worse because many poor and illiterate farmers are sometimes misinformed about basic hygiene.
Villagers are reported to be reluctant to hand over birds
Dead birds are reported to have been dumped in village wells and ponds by people not aware of the risks from the H5N1 virus.
Federal officials have warned that if the pace of culling does not pick up fast, the airborne virus may spread to the remaining districts and even hit Calcutta.
One of the districts most recently affected, Hooghly, is close to Calcutta and contains the state's largest chicken hatchery.
"If this spreads to Calcutta, there will be panic and chaos," animal disease expert Barun Roy said.
The municipal authorities in Calcutta are not prepared for such a situation, he said.
'Panic and chaos'
Another district recently hit by the virus, Coochbehar, is close to the border with Bangladesh.
West Bengal has sealed a stretch of its border with Bangladesh, which has been fighting to contain the spread of bird flu since March last year.
Experts in Bangladesh have warned that the outbreak of the virus is far worse than the government is reporting.
"Bird flu is now everywhere. Every day we have reports of birds dying in farms," leading Bangladeshi poultry expert MM Khan has said.
"Things are now very serious and public health is [in] danger," he said, alleging that farmers were reluctant to report new cases.
There is little evidence that the virus can be transmitted easily between humans.
Most human victims have contracted the disease through close contact with affected birds.