The fresh demand comes a day after the BJP government in Jharkhand banned the PFI for its alleged links with the terrorist group Islamic State.
Accusing the Congress government of minority appeasement, leader of the opposition in the Karnataka assembly Jagadish Shettar said, "Already they (the Congress government) have dropped the cases against PFI. This is with malafide intention and for political gain. So many Hindu people have died, but the Congress is always supporting PFI. It is their intention to get minority votes".
Chief Minister Siddaramaiah was brief in his dismissal of the issue. "The situation is not here in Karnataka," he said, when asked about a ban on PFI in the state.
In October 2016, Rudresh, an RSS worker, died after he was attacked with machetes in Bengaluru. Police arrested five people within a month, all members of the PFI and its political wing, the Social Democratic Party of India (SDPI).
A month later, the central government ordered a probe by the National Investigation Agency (NIA). In its chargesheet, the agency said the murder was an act of terrorism.
Mr Siddaramaiah has dismissed the allegations, accusing the BJP and RSS of creating communal tension and trying to disturb communal harmony.
Asked whether the state government would ban PFI, Law Minister TB Jayachandra said, "There should be some proof. If there are positive reports, then only we can think of it. And that applies not just to one institution but to all."
Assembly polls are due in Karnataka by May and the BJP is hoping the reclaim the only state in south India that it ruled from 2008 to 2013.