Accusing the state police of failing to control the situation, party general secretary Kailash Vijayvargiya, who is also in charge of the state, urged Home Minister Rajnath Singh to intervene in the matter.
West Bengal Chief Minister Mamata Banerjee has said communal violence broke out over an "objectionable" post on Facebook. The Centre too has sent 300 paramilitary personnel to the state.
Vijayvargiya blamed Muslims for the violence in his letter to Singh.
As the troubled spot is adjacent to Bangladesh, there is a possibility that "outsiders" were involved in this violence, he said.
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"The local police appears unable to control the situation," he said.
Banerjee said in Kolkata that clashes between members of two communities broke out in Baduria in the Basirhat sub- division of the district over the post.
It has projected itself as the protector of Hindu interests and accused Banerjee of pandering to Muslims.
The West Bengal chief minister has stoutly refuted BJP's allegations and accused it of "playing religious politics" to polarise votes for political benefits.