The Delhi High Court has ordered the companies to present their plans for policing their services in the next 15 days, ZDNet.com reported Monday.
In the meantime the Indian government has requested voluntary efforts to keep offensive material off the Internet, and Google and Facebook said they have complied by removing objectionable content.
India passed a law last year making companies responsible for content posted on their Web sites by users, requiring them to take down "ethnically objectionable," "blasphemous," or "grossly harmful" material in case of a complaint.
While civil rights groups decry the law, politicians say posting offensive material in the socially conservative country presents a danger to the public given India's history of violence between religious groups.
Trying to use the Internet to spur India's economy and raise living standards for its 1.2 billion people while accommodating conservative religious and political sentiments is proving difficult, analysts say.
The case before the court grew out of a private complaint filed by journalist Vinay Rai against 21 social networking sites allegedly showing images that seek "to create enmity, hatred, and communal violence" which "will corrupt minds."