In another statement, the party called the rigging "a grave affront to parliamentary democracy" and said people's faith in electoral process "can only be restored if a re-poll is conducted" in the affected booths.
This should be done "with proper deployment of central paramilitary forces so that people can vote freely and fairly", it said.
The CPI-M also demanded a proper process to identify and apprehend those responsible for "grave malpractices and the consequent gross distortion of the election process".
It said that of the 17,330 polling booths where polling was held Wednesday, only 324 had video surveillance. This issued must be addressed during re-poll, it said.
"This assault of democracy cannot be allowed to go unpunished."
Asked if the CPI-M had been guilty of the same strong-arm tactics it was now accusing the state's ruling Trinamool Congress of, party politburo member Sitaram Yechury said that "if we had used these tactics, they wouldn't have been in power".