Naqvi, a muslim face and Vice President of the party, termed Ali's entry into BJP as a "mistake" and demanded its reversal.
BJP spokesman Sudhanshu Trivedi said the induction was done on the recommendation of Bihar unit of the party and "further action" in the matter will be taken after "verifying all facts and antecedents" of Ali.
"Whatever has happened today, I am pained and have already expressed my anguish in the party. Somewhere there has been a mistake committed by the party and the party needs to correct that by reversing the decision," Naqvi said later.
The new row comes days after the one over induction of Sri Ram Sene chief Pramod Muthalik in Karnataka. The entry was scrapped within hours after strong criticism from both within and outside the party as Muthalik had been involved in attack on women in pubs few years back.
He alleged that Bhatkal was arrested from Ali's Mumbai residence some time ago, even as his name had figured in the murder case of noted music magnate Gulshan Kumar.