"Congress is trying to create an atmosphere of violence and fear among opposition parties as it is in a troublesome position over the UPA government's anti-people policies and unfulfilled promises in the constituency," CPI(M) state secretary Biman Bose said.
"I condemn the murder of comrade Hamid Sheikh, a primary school teacher, who was killed only to instill fear in the minds of people," Bose said.
Sheikh, shot dead on Saturday night by unknown assailants, was the party's Shibpur local committee member in Murshidabad district.
Bose claimed that Congress leaders and workers were angry over the huge attendance at a party rally at Nabagram within the Jangipur constituency.
Election to the Jangipur constituency was necessitated by Pranab Mukherjee's resignation before being elected President.
Bose also alleged that the police was playing a partisan role and demanded that the force take immediate steps to arrest the culprits.