Referring to revocation of Paricharak's suspension by the Council last week, Parab said it was done amidst an uproar and that there was no need to lift the suspension.
Paricharak was suspended from the Upper House in March last year, after he joked during an election campaign about wives of soldiers.
The legislator had later apologised for his statement.
"Paricharak should be dismissed as he has insulted the soldiers and their wives. His comments are unforgivable," said Parab.
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"There was no need to pass the proposal revoking his suspension. It was done so amidst an uproar. Paricharak has committed a crime worse than that of a traitor. His act is unforgivable and hence I am submitting a new proposal seeking his dismissal," the Sena MLC said.
Senior Sena member Neelam Gorhe termed as "untrue" Revenue Minister Chandrakant Patil's statement that a committee set up to examine Paricharak's remarks had unanimously recommended revocation of his suspension.
Echoing Gorhe, JD (U) MLC Kapil Patil said the proposal to lift the suspension was not cleared unanimously.
Leader of Opposition Dhananjay Munde said Parab's proposal can be moved as it is not contradicting the resolution passed by the Upper House (in March last year) to suspend Paricharak.
"The council had passed the resolution to suspend Paricharak whereas the new proposal seeks his dismissal. So there is no contradiction. After all, it's the discretion of the council chairman whether to accept (Parab's) proposal or not," Munde said.
Meanwhile, a war of words broke out between Kapil Patil and Chandrakant Patil (BJP) on the issue of revocation of suspension after the JD(U) MLC said the Paricharak issue is serious "given that those who traditionally use such (derogatory) words are in power".
Later, Chairman Ramraje Nimbalkar adjourned the House for 10 minutes.
When the House reassembled, Panel Chairman Neelam Gorhe adjourned the proceedings for the day.
Meanwhile, a senior legislative official told PTI outside the Council that Parab's proposal may not see the light of day.
"As per rules, if a private member moves a proposal it goes for a ballot first. The chairman has discretionary powers to take a decision on whether the proposal should be considered for discussion. There is no deadline for this procedure," he said.
"In this case, Parab's proposal will not stand on the parameters set by the existing rules," he added.