A bench of Justice B D Ahmed and Justice Sanjeev Sachdeva granted three week's time to the government and asked it to file the reply "positively" on the issue.
The court fixed the matter for further hearing on March 13.
Advocate Virag Gupta, appearing for Govindacharya, raised objection on usage of Facebook and Twitter for official purpose by several ministries through private e-mail accounts, saying it violates the Public Records Act as per which "no person shall take or cause to be taken out of India any public records without the prior approval of the central government".
During the hearing, Additional Solicitor General Sanjay Jain, appearing for the Centre, said it had called a meeting of social media companies on January 23 and the issue is being examined.
The court was hearing a PIL filed by Govindacharya who that contended government departments are not entitled to creating accounts on social networking sites.
The PIL also sought recovery of taxes from the websites on their income from operations in India.
It alleged that the sites have no mechanism for protection of children from online abuse.
