The Indian parliament is expected to consider the resignation of Rajeev Shukla, who was sacked on Thursday after being accused of sexual harassment.
Mr Shuklas is the first minister to resign after the current parliament, the lower house, was formed in 2015.
He has denied all the allegations.
Mr Rajya Sarakalwal, a member of the Rajya Rajya Sangh (RRS), said he has asked his party colleagues to join the RRS, which has an alliance with the Congress.
The BJP has called for Mr Shukles resignation and has asked the Supreme Court to block the resignation.
The ruling Congress party has criticised the move as political opportunism and accused the BJP of being behind the move.
In the past, the RSS has supported former chief minister Mamata Banerjee, who resigned after her husband, former Union minister and former Finance Minister P Chidambaram, was accused of sexually harassing her.
Ms Banerji was later reinstated by the Rajasthan government.
The Bharatiya Janata Party (BJP) had also said that it had written to Mr Shulkas ex-wife.
The Rajya Bharati Congress (RBC), a rival political force, has also called for his resignation.
Mr Bharati’s party has accused the RBC of being politically motivated.
The RBC said that the party will continue to work to support Mr Shoukla and the party has also asked the party’s national executive committee to vote on his resignation in the coming days.
Mr Mukherjee, a close aide of Mr Shikals wife, has resigned as the party chief after a petition was filed by the wife.
The RBC has also decided to put pressure on the Congress to withdraw its support.
The BSP and BJP have also said they will vote against Mr Shulipur, the party president, in the Rajda Sabha.
The BJP had earlier announced it would expel Mr Shuls father-in-law from the party.