In the notice, the government told the BBC that it has "violated" the agreement of not using the documentary for commercial purpose and for this the British media giant was liable for legal action.
"No necessary approval was taken by the BBC for the commercial use of the documentary. We have served the notice and waiting for their response. Further course of action is awaited," a Home Ministry official said.
It was served by Director General of Tihar jail Alok Kumar Verma through government standing counsel.
Officials claimed that filmmaker Leslee Udwin had agreed to the condition that the documentary would not be used for commercial purposes. However, she sold the rights of the film to BBC allegedly allowing it for using commercial purpose.
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Earlier in the day, government said necessary action will be taken as the BBC ignored its advice and broadcast the controversial interview of Delhi gangrape convict.
Home Minister Rajnath Singh also spoke to Communication and IT Minister Ravi Shankar Prasad asking him to ensure that the video is removed from all social media sites.
BBC aired the documentary, containing the controversial interview of a convict in the December 16,2012 gangrape despite a Delhi court prohibiting it.