The virus has been detected in 13 of the eastern state's 19 districts since the outbreak began in mid-January.
Nearly three million poultry had been due to be slaughtered by late Saturday, but authorities said that after the fresh outbreak the exercise was now expected to be completed by Monday.
"It's not alarming. It will be possible to contain the spread of the disease by Monday," West Bengal animal resources development minister Anisur Rahaman told AFP in the state capital Kolkata.
"Culling teams are working on a war footing to meet the deadline," the minister said.
No cases of human infection have been reported so far.
"Nearly 800 culling team members have already been quarantined in different state-run hospitals," state health minister Surya kanata Mishra said, adding a total of 5,000 workers would be isolated after the slaughter was over.
As a precautionary measure however, the workers were being administered Tamiflu, recommended by the World Health Organisation as a first line of defence against the virus, the minister said.
Humans typically catch bird flu by coming into direct contact with infected poultry, but experts fear the H5N1 strain may mutate into a form easily transmissible between people.
Culling operations also started at the weekend in neigbouring northeastern Assam state as a precautionary step.
An estimated 85,000 poultry were due to be culled in the next 10 days in 40 villages close to the West Bengal border, Assam state officials said.