Education Minister Partha Chatterjee said attempts were made to create unrest in Raniganj and Asansol and the administration had handled the situation there.
He warned that steps would be taken by the administration against those violating the law.
"The BJP is fomenting unrest in the state using the name of Lord Rama," Mr Chatterjee, who is also the TMC secretary general, said.
On the Centre seeking a report on the violence from the state government, Mr Chatterjee said he was not aware of any such move.
Asked about the central government's offer to send paramilitary forces to the state, he said, "Media reports have mentioned the Centre's offer but a decision in this regard has to be taken by the chief minister ... We are competent and had tackled many difficult situations in the past".
The centre has sought a report from the West Bengal government on incidents of arson and violence during Ram Navami processions earlier this week and offered assistance to deal with the situation, an official spokesperson said.
Accusing the BJP of fanning trouble in the state, Mr Chatterjee said the party workers could take out processions but should not carry arms.
Referring to state BJP president Dilip Ghosh's allegation that its workers were provoked by the police, he said, "They had carried arms. Is it then a provocation if the police took action? Action will be taken if there is any violation of law."
On the BJP's charge that the chief minister was away in Delhi when there was trouble in the state, Chatterjee said, "She is there in the interest of the people. She is there to share the people's agony created by the BJP."
Meanwhile, Prakash Javadekar told reporters in New Delhi that Trinamool Congress "thugs" had attacked peaceful Ram Navami processions in West Bengal.
"Bengal is burning and Mamata is doing politics in Delhi. It is like Nero fiddling while Rome was burning," he said.