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Her comments came a day after state Director General of Police Surajit Kar Purakayastha claimed to have got intelligence inputs about outsiders entering the state to foment violence and unrest.
"We have inputs that some people may come here to create violence and disrupt the peace. We are keeping an eye on them according to our intelligence input. If anyone tries to create any sort of unrest or disturbance we will take strict actions against them," Purakayastha said after a high-level meeting on Friday.
Banerjee cautioned the people not to get "misled" by conspiracies hatched by troublemakers.
"Please be alert and active in countering mischievous tweets and Facebook posts which may try to spread falsehood and misinformation."
She said embracing festivals of all communities was intrinsic to the state, which abhors conflicts.
"One shouldn't spare those troublemakers who are trying to besmirch our reputation, our Durga Puja festival."
Banerjee said during the recent communal disturbances at Baisrhat of North 24 Parganas district "some elements had issued video clips from Bhojpuri films to claim the incidents had taken place in Bengal" and "also tried to pass off some happenings in neighbouring Bangladesh as incidents in occurring in Bengal."
Slamming those raising questions about her religion, she said she "hated their poor taste".
Banerjee said in April, a priest had tried to block her entry to the famous Jagannath Temple in Puri. "But others then took me inside."