As his twitter posts triggered an outrage, Varma took to the microblogging website to tender an apology.
The 52-year-old producer and director, who apart from questioning the ability of Ganesha to remove obstacles from the path of his devotees, made fun of his physical attributes.
Varma's comments drew strong reactions from leaders across the political divide.
While Shaina N C of the BJP called it "blasphemous and insensitive", Congress' former MP from Mumbai Sanjay Nirupam demanded police action against him for violating the law of the land.
"He has hurt the religious sentiments of the people. We have great faith in Ganesh. Nobody has the right to make such statements.
"Ram Gopal Varma has not been able to give a hit film in a long time. He wants to remain in the news and so is making such statements. As he has violated the law of the land, police must take action against him," Nirupam said, adding "he (Varma) is known for such publicity stunts".
He also questioned the timing of the tweets. "His comments at this time are intentional and merit criminal action against him. This is a cheap and dirty way to be in the news. This will create social disharmony," Shukla said.
As the director-producer faced an avalanche of criticism, he, in another twitter post said," All tweets I put on Ganesha were in my usual manner but unintended by me to hurt anyone's sentiments...But if they did I sincerely apologize."
The visit had created a nationwide outcry and ultimately led to Deshmukh's resignation.
Varma denied that he had plans to make a film but eventually came up with a movie titled 'The Attacks of 26/11' in 2013.
