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 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 media, of course, always loves the latest news. But that is no reason to abandon worthwhile causes halfway without taking them to their logical conclusion
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.
Solicitor General Tushar Mehta said those involved in terror activities may take pre-emptive steps if the government divulges details of which software is used for various purposes.
A bench headed by Chief Justice N V Ramana sought the Centre's response on the pleas and said it will take up the matter after 10 days and see what course should be adopted.
With a view to dispel any wrong narrative spread by certain vested interests and with an object of examining the issues raised, it said, the government will constitute a committee of experts.
Minister of State for Defence Ajay Bhatt, while replying to a question in Rajya Sabha on Monday, said, "Ministry of Defence has not had any transaction with NSO Group Technologies."
Malik told reporters here that the Defence Ministry has said there was no transaction with the NSO Group, an Israeli surveillance software company, regarding the Pegasus spyware.
'Have faith in the system': Supreme Court takes exception to parallel debates over Pegasus on social media
Solicitor General Tushar Mehta, appearing for the Centre, told the bench that he needed some time to take instructions from the government on the issue raised in the petitions.
The opposition members, however, insisted that the Pegasus matter be taken up for discussion and trooped into the Well.
In its first response to the Pegasus snoopgate controversy, the Ministry of Defence on Monday said it did not have any transaction with Israel-based NSO Group, which owns the spyware.
NSO Group has been under increasing attack following allegations that its Pegasus software was used for surveillance of phones of people in several countries, including India.
The video compiles these statements made by the opposition MPs in the Upper House, with the words "farmer" and "Pegasus" in the opening lines.
Talking to reporters in Delhi, Raut expressed surprise that the central government was not even paying heed to the Supreme Court's observation that the Pegasus case, if true, was a serious matter.