The filing of nominations, which began at 11 am, will continue till 3 pm.
The Calcutta High Court had on Friday directed the State Election Commission (SEC) to extend the date.
The SEC issued a fresh notification on Saturday announcing April 23 as the new date for filing nominations to the three-tier panchayat elections.
"The nomination process has began and we have received a few complaints and are looking into them. We have also formed a control room to address those problems," a senior SEC official said.
The SEC has asked the police to make adequate security arrangements to prevent any untoward incident during the filing process.
The opposition Congress and the BJP accused the Trinamool Congress of "letting loose a reign of terror" since the morning to prevent their candidates from filing their papers.
The opposition parties alleged that incidents of violence had occurred in Murshidabad, Malda and South 24 Parganas districts.
A senior TMC leader brushed off the allegations as "baseless" and blamed the opposition for "vitiating peace" in some parts of the state.
The dates for the polls, which were earlier scheduled to be held on May 1, 3 and 5, are yet to be announced by the commission.
The nominations received today would be scrutinised on April 25. The last date for the withdrawal of candidature is April 28, the notification had said.
Get Breaking news, live coverage, and Latest News from India and around the world on NDTV.com. Catch all the Live TV action on NDTV 24x7 and NDTV India. Like us on Facebook or follow us on Twitter and Instagram for latest news and live news updates.