GJM chief Bimal Gurung challenged Banerjee to stop the agitation in the hill and said that it was his writ that "runs in the hill". He also projected himself as the "chief minister of the hills".
In all six columns of Army have been deployed, three in Darjeeling, two in Kalimpong and one in Kurseong, a defence spokesperson said.
The Army was requisitioned by the state government for Kurseong and Kalimpong as a precautionary measure, besides Darjeeling town which saw large-scale violence and vandalism yesterday.
The Army carried out flag marches in Darjeeling, Kalimpong and Kurseong, he said adding that the situation was under control of the civil administration.
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The hill station of Darjeeling, brimming with tourists, had witnessed violence yesterday when GJM supporters clashed with the police and burnt police and government vehicles.
Shops, eateries and markets remained closed in the hill although the state government has made arrangements for buses to help the tourists to come down to Siliguri.
Mamata Banerjee, who stayed back here after yesterday's cabinet meeting, asked the tourists not to get scared.
She said arrangements have been made to help the tourists to return to Siliguri from Darjeeling. The state government has also arranged buses to carry the tourists from Siliguri to Kolkata, she said.
"I will ask the tourists not to worry, the government is there for you", Banerjee who visited some areas, said.
"I have seen how so many vehicles were set on fire. We want peace and development in the hill. The Army has already started route march", she said.
Last night, an FIR was filed under non-bailable sections at Darjeeling Sadar police station against Gurung and GJM general secretary Roshan Giri.
The GJM supporters had protested alleging that the state government was imposing Bengali language in the schools in the hill which was refuted by the Chief Minister.
She said the Bimal Gurung-led Gorkhaland Territorial Administration (GTA) has failed to carry out any development work in the Hill and now when their term is scheduled to be over next month, they have started "torturing the public".
Urging the people in the hill not to support Gurung, she said GJM was scaring away the tourists from the hill which would affect the people who thrive on tourism.
The Chief Minister, who visited the injured police personnel in hospital, said the state government will give compensation to their families and bear their medical expenses.
She said one police personnel, who received injuries in his eyes during yesterday's violence, will be airlifted to Kolkata for further treatment. If necessary, he would be taken abroad for treatment, she said.
"I will talk to the Centre, we are an ally of NDA. We will give them all the details of police atrocities on the innocent people of the hills," he said.
When asked about deployment of Army in Darjeeling, West Bengal Governor KN Tripathi, said in Kolkata,"I am yet to receive any official communication.