She also alleged that the Centre provides a lot of assistance for holding Kumbha Mela but is not doing so for the Gangasagar Mela.
"Some people come to foment trouble as they don't have any other job. Don't do anything which creates an atmosphere of riot. I will give my life but never allow anyone to indulge in wrong doings," Banerjee said at the Vivek Chetana Utsav.
Addressing a gathering of Gangasagar-bound pilgrims at the Utsav here, the chief minister also asked people not to do anything which tarnishes Bengal's image before lakhs of pilgrims from different parts of the country.
The police had not granted permission for the event in view of the Gangasagar Mela and the Bharatiya Janata Yuva Morcha moved the Calcutta High Court and secured its nod to hold the rally between January 12 to January 18.
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"Can there be a rally when our sole direction should be focused on conducting the Gangasagar Mela successfully?" Banerjee asked.
"Some people from Delhi, someone from a party like BJP may utter many things. But don't believe in their words. Why should they take out the rally? Their sole aim is to create disturbance. We want peace and not riots in the name of Swami Vivekananda," the chief minister said.
The central government has not declared national holidays on the birthdays of Swami Vivekananda and Netaji Subhas Chandra Bose, she said at the programme attended by monks of the Ramakrishna Mission, the Bharat Sevasram Sangha and other organisations.
Stating that Gangasagar Mela is a big congregation after Kumbha Mela, Banerjee blamed the Centre for doing nothing to help improve facilities at this spot.
"The Centre provides so much help for Kumbha Mela but not to Gangasagar. Now the West Bengal government is doing everything possible for the pilgrims by improving amenities," she said.
Besides abolishing a tax collected by the previous Left Front government from Gangasagar pilgrims, the Trinamool Congress regime has arranged for an insurance cover of Rs 5 lakh in case of any untoward incident during the three days of the mela, she said.