The pleas seeking an independent probe are related to reports of alleged snooping by government agencies on eminent citizens, politicians and scribes by using Israeli firm NSO's spyware Pegasus.
Apple has released a critical software patch to fix a security vulnerability that researchers say could allow hackers to directly infect iPhones.
Researchers at the University of Toronto's Citizen Lab said they had high confidence that the world's most infamous hacker-for-hire firm, Israel's NSO Group, was behind that attack.
Solicitor General Tushar Mehta said the Centre did not want matters of national interest to be part of public discourse or judicial debate through an affidavit.
The court was told by senior advocate Kapil Sibal, appearing for N Ram and Sashi Kumar who have filed one of the pleas, that the government can't tell the apex court to 'shut your eyes'.
The government told a bench that the disclosure whether the country is using a particular software or not may cause 'harm' and alert all potential targets.
The pleas are related to reports of alleged snooping by government agencies on eminent citizens, politicians and scribes by using Israeli firm NSO's spyware Pegasus.
The Centre had earlier filed a limited affidavit in the apex court saying the pleas seeking an independent probe into the Pegasus snooping allegations are based on 'unsubstantiated media reports'.
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The court had issued a notice to the Centre on the pleas on August 17, while making it clear that it did not want the government to disclose anything which compromises national security.
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The Monsoon Session of Parliament was ransacked by the Opposition, calling use of Pegasus spyware an attack on their freedom and privacy.
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The State government in its affidavit has called the Union government "non-committal and evasive" while justifying the setting up of a two-member Commission of Inquiry.
Those reportedly hacked included members of the Bahrain Center for Human Rights and two political dissidents living in exile.