A short video clip of Siddiqui's speech, at a function last week, has gone viral on social media.
The veteran leader can be heard saying "I wish to cite a personal example to highlight the country's atmosphere (desh ka jo mahaul hai). I have a son who is studying at Harvard and a daughter who is a London School of Economics pass out. I have told them to find jobs abroad and, if possible, even take foreign citizenships".
A former state minister, Siddiqui can be heard adding "when my children reacted with disbelief, pointing out that I was still living here (in India) I told them they will not be able to cope".
Though the RJD leader cannot be heard making a direct reference to Muslims and their condition under the BJP rule, the saffron party took the bait.
"Siddiqui's remarks are anti-India. If he is feeling so stifled, he should give up the privileges he enjoys here as a political leader and move to Pakistan. Nobody will stop him", fumed state BJP spokesman Nikhil Anand.
"Siddiqui is a close aide of RJD supremo Lalu Prasad and his utterances are reflective of his party's culture of Muslim appeasement", added the BJP leader.