"The polling started at 7 in the morning," the official said.
Polling will end at 5 pm. The counting will take place on May 17.
It is the last major polls in the state before the next year's Lok Sabha elections.
With 40 of the 42 Lok Sabha seats located in the districts, political parties are viewing today's event as a warm up match ahead of 2019 general elections.
After a protracted legal battle in the Kolkata High Court and the Supreme Court involving the State Election Commission, the ruling Trinamool Congress and the opposition parties, the three-tier panchayat polls in West Bengal is being held.
The run-up to the panchayat polls was marked by intense campaigning. The ruling Trinamool Congress was engaged in a bitter war of words with the opposition Congress, Left Front and BJP over the violence that erupted during the filing of nominations for the polls.
The opposition had accused the ruling TMC of letting loose a reign of terror during the nomination process. The TMC rubbished the allegations and had said the opposition do not have a mass base and are trying to evade the polls.
The filing of nominations, which was held from April 2 to April 9 and then again on an extended date on April 23, was marked by violence and clashes between the ruling TMC and opposition parties that led to several deaths.
Banerjee appealed to the people to vote in favour of development ushered in by her government.
According to the State Election Commission (SEC) sources, today's elections are being held in 621 zilla parishads and 6,157 panchayat samitis, besides 31,827 gram panchayats.
According to West Bengal SEC sources, of the 48,650 seats in 3,358 gram panchayats, 16,814 were uncontested and of the 9,217 seats in 341 panchayat samitis, 3,059 were uncontested.
In the 20 zilla parishads, 203 of the 825 seats were uncontested, the SEC said.
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