"We have decided to postpone counting of votes," State Election Commissioner Susanta Upadhyay told newspersons at the SEC office in Kolkata.
The counting of votes in the elections held on Saturdya was scheduled to be conducted on October 7.
The SEC also postponed counting of votes for elections held in Bally under Howrah Municipal Corporation.
While Bidhannagar is in the eastern flank of Kolkata, Howrah is on western side across the river Hooghly.
Upadhyay said the SEC would go through reports and video footages of violence from its own sources and also news channels before taking any further decision.
Opposition parties in the state have demanded that the elections be countermanded and fresh elections held, alleging large-scale violence by the ruling Trinamool Congress.
To a question on repoll, Upadhyay said, "There is no question of ordering repolls at this juncture. We will take a decision after going through reports and video footages."
Counting for elections held in wards of Siliguri Mahakuma Parishad would be held as per schedule, he said.
A blame game has ensued between the ruling Trinamool Congress and opposition parties over violence during Saturday's elections.
The TMC today "blamed" the Communist Party of India-Marxist for violence during Saturday's civic election in a counter to the opposition parties' demand for re-election to the two civic bodies alleging loot of votes by the ruling party.
"The CPI(M) is responsible for the violence, it was a planned attack by it owing to desperation as it knows that it will be defeated in the elections," senior TMC leader and state Panchayat minister Subrata Mukherjee told newspersons at the party headquarter here.
Alleging that CPI-M leader Gautam Deb, a former minister, had threatened to bring in four to five thousand outsiders for the polls held yesterday in Bidhannagar, Mukherjee said, "It is the CPI-M which instigated violence."
TMC secretary-general Partha Chatterjee also "blamed" the CPI-M for yesterday's violence at Bidhannagar and Asansol.