"If I open my mouth, a lot of people will be in trouble," Kumar told reporters on the sidelines of a programme.
BJP President Rajnath Singh, who addressed a party rally on Sunday, had trashed JD-U's allegations that Narendra Modi was an autocratic and divisive leader.
He had attacked the JD-U for 'suddenly' finding fault with the Gujarat chief minister and his leadership after being part of the alliance for 17 years.
The BJP President had also questioned Kumar's growing proximity to the Congress.
Singh's predecessor Nitin Gadkari has accused Kumar of playing vote bank politics to fulfill his prime ministerial ambitions.
Former deputy chief minister Sushil Kumar Modi, former NDA convenor Nandkishore Yadav, Rajiv Pratap Singh Rudy, Shahnawaz Hussain, Ravishankar Prasad, C P Thakur and state BJP President Mangal Pandey have also been firing verbal salvos at Kumar.
The acrimony had widened so much that workers of the JD-U and the BJP clashed on the streets of Patna during the Bihar bandh on June 18.
BJP MLAs had unleashed a verbal attack on Kumar during the confidence vote.
After the JD-U snapped ties with the BJP on June 16, Kumar had said political issues should be answered politically and advised leaders of both parties not to point fingers at each other.
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