The anti-terror investigation agency is also set to summon Mr Naik, who is abroad ever since his name cropped up linking terror activities following the Dhaka terror attack on July 1.
Search operations were carried out by the NIA at the offices of IRF, premises of Mr Naik as well as that of Harmony Media Private Limited, from where the programmes were being aired on Mr Naik's Peace TV.
The NIA also blocked the IRF's website, which was allegedly promoting "hate speeches".
"As part of investigation, all actions that need to be taken against a proscribed organisation, including banning of its online activities, are being undertaken," an NIA spokesperson told Press Trust of India.
Last week, the Centre banned the IRF and declared it as a terrorist organisation under the Unlawful Activities Prevention Act for five years.
If the Islamic preacher fails to respond to the NIA summon, a red corner notice will be issued against Mr Naik through Interpol.
The NIA is still trying to block Mr Naik's Facebook page, Twitter account and YouTube videos that contain alleged "objectionable" material and may seek help from authorities in the US where the servers of Internet giants like Google and Yahoo are located, officials.
The agency is expected to examine cases relating to 50 individuals who were allegedly drawn to extremism after listening to Mr Naik's sermons.
Zakir Naik has been booked along with unnamed IRF officials under section 153-A of IPC (promoting enmity between different groups on grounds of religion and doing acts prejudicial to maintenance of harmony) beside various sections of UAPA.
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