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 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 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'.
Many regional leaders have national aspirations and issues like Pegasus spyware that united them may not resonate on the ground to as far as electoral fortunes are concerned.
Pitching for a discussion on the Pegasus issue, opposition parties have repeatedly disrupted the proceedings in Parliament, resulting in frequent adjournments in both houses.
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."
'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.
Pawar started replying to a question, but members of the opposition raised the Pegasus snooping and farm laws issues and protested against the government.
PIL questions Maharashtra officials' 2019 Israel tour; lawyer claims it was to acquire Pegasus-like spyware
Several rules regarding the sanctioning of such foreign tours were violated in the process, the Public Interest Litigation alleged.
Addressing a 'Sansad Gehrao' protest here by the Indian Youth Congress, he targeted the prime minister over the issue of employment too.
The Opposition also unequivocally conveyed that the discussion on the farmers’ issues and agitations arising from the three laws should follow the discussion on Pegasus.
18 leaders from 14 parties said that it is unfortunate that the government has 'unleashed a misleading campaign to malign the combined opposition'.
Echoing the Opposition demand, Kumar said since the issue has been raised for so long, it should be discussed.