A bench of Chief Justice Dipak Misra and Justices A M Khanwilkar and D Y Chandrachud said the matter will be listed in due course of time.
In a bid to bring in transparency, the top court had last year allowed the installation of CCTV video recording with audio in trial courts and tribunals of each state.
Senior advocate Indira Jaising, appearing in person, said that the citizens have the right to information and matters of constitutional and national importance can be live-streamed.
If live streaming of top court's proceedings is not possible, then alternately the video recording should be allowed, she said.
Jaising said that like the top court is currently hearing Aadhaar matters and will be hearing other constitution bench matters which are of great significance to the people, the proceedings can be live streamed.
"This Writ Petition is filed as Pro Bono for enforcement of public interest, to advance the rule of law and bring accessibility and transparency in the administration of justice," her plea said.
"The Petitioner submits that the live streaming and videography of the proceedings of the Supreme Court in matters of great public importance will be in keeping with the principle of open access to justice and will ensure justice is not only done but it is seen to be done," her plea said.
She said the apex court may place restrictions on such videography and live streaming of proceedings, in cases where there are "countervailing interests of privacy as in family law cases, criminal law cases, as well as in the interests of witness testimonies in criminal matters".
In her plea, Jaising contended that a cardinal principle of law is that justice is not only to be done in public but also should be seen to be done and the best possible manner to achieve this goal is to live stream the proceedings so that the arguments of all counsels are heard and recorded.
Such an exercise would inspire confidence in the functioning of the judiciary as an institution and help in maintaining the respect that it deserves as a co-equal organ of the state, she said in her plea.
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