The clashes took place at Baharampore and Domkal in Murshidabad district, while instances of scuffle were also reported from other parts of the state.
Train services of South Eastern Railway and Eastern Railway were partially affected due to the strike, but Metro Rail services in the capital city remained normal.
State government buses and trams plied on the roads but there were less private buses, minibuses and taxis. Most shops, markets and business establishments remained closed.
Banerjee said "the bandh failed to evoke any response and state government offices in the city recorded 93 per cent attendance and 97 per cent in the districts".
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However, members of the ruling Trinamool Congress and the main opposition CPI-M clashed at Baharampore and Domkal in the Murshidabad district.
Police said there were incidents of stone-pelting and use of low-intensity bombs at some places in Murshidabad. Six CPI-M workers were arrested in this connection.
TMC's Murshidabad district president Mannan Hossain denied the allegation and claimed that CPI-M had attacked his party workers and his car was damaged.
Asked about Murshidabad violence, Banerjee said, "People carrying red flags were seen beating TMC workers. CPI-M tried to create violence but our workers have shown restraint. Why should Trinamool workers resort to violence?"
Accusing TMC government of using "brutal force to break the general strike", the state Left Front Chairman Biman Bose said Banerjee's stringent opposition against the strike call was because of her intention to present herself as a loyal ally of BJP at the centre.