Agrawal, who lost out to Bachchan in the race for re-nomination to the upper house, today quit the Samajwadi Party and joined the BJP.
"I have been reduced to somebody working in films. For somebody who used to dance in films, act in films, I was denied a ticket (for Rajya Sabha). I did not find it appropriate," Agrawal said while joining the BJP at its headquarters.
BJP spokesperson Sambit Patra distanced his party from Agrawal's remarks, saying it respects people from all fields and welcomed them in politics.
A couple of hours later, senior BJP leader and its most prominent woman face Sushma Swaraj took to Twitter to criticise Agrawal's comments.
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"Naresh Agrawal has joined Bhartiya Janata Party. He is welcome. However, his comments regarding Jaya Bachhan ji are improper and unacceptable," the external affairs minister tweeted.
Agrawal, who was in the Congress earlier, is not new to controversy. Last year, the BJP was up in arms over his remarks in the Upper House mocking Hindu gods.
He expressed his affection for SP patriarch Mulayam Singh Yadav and his cousin Ram Gopal Yadav, saying he could never leave them. Apparently criticising SP president Akhilesh Yadav, he added that it was losing strength in Uttar Pradesh due to its decision to ally with other parties.
Agrawal said he was joining the BJP unconditionally, and asserted that his MLA son would support the saffron party in the Rajya Sabha elections in the state.
He expressed his admiration for Prime Minister Narendra Modi and UP Chief Minister Yogi Adityanath.