Ranragini, which has affiliation to Hindu Janajagruti Samiti, filed a complaint with Mapusa police last evening with its local office-bearer Vishakha Mhambare demanding that Varma should be booked under Cyber laws and section 292 of IPC.
Varma, who is not new to social media feuds, tweeted yesterday, "I wish all the women in the world give men as much happiness as Sunny Leone gives."
The complaint said Varma has gravely insulted women with his tweet on the International Women's Day.
Police Inspector Rajendra Prabhudesai, who is probing the complaint, said he is examining the case.
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Varma said he will file a counter suit against Mhambare for "disrespecting 18 lakh followers of @SunnyLeone."
He later got into a war of words with NCP MLA Jitendra Awhad on Twitter. Awhad asked Varma to apologise or "face the consequences, we don't mind taking law in hand (sic)."
To which, the director replied, "If you don't apologise to threat of taking law into your own hands, will formally register complaint, so let me know. Please note."
Meanwhile, Congress today demanded that the Maharashtra government and State Women's Commission file an FIR against the filmmaker for his "sexist" remarks.
Senior Congress leader and former state minister Mohammed Arif Naseem Khan told reporters that Varma had tweeted from Mumbai.
"Hence the state government and State Women's Commission should take cognisance of the comments and file an FIR against him," he said.