While blaming BJP, RSS and ABVP for the violence, Congress legislative party leader Pradeep Mathur raised the matter of Rai's release thorough an adjournment notice during the Zero Hour.
The allegation evoked sharp reactions from BJP members.
Rai was arrested on October 6 for his alleged role in the violence and arson in Varanasi during a march by seers and other local leaders against police action on protesters opposing ban on immersion of Ganesha idols in the Ganga river.
State Parliamentary Affairs Minister Azam Khan, however rejected the adjournment notice and assured Congress that the government would consider invoking National Security Act (NSA) against the MLA.
"Sending any MLA to jail on such charges is not welcome ..Government is ready to re-consider the case on basis of its merits and demerits," he said.