"Every aspect of it does not qualify as a fundamental right, as privacy also includes the subtext of liberty," said the centre's lawyer KK Venugopal.
A nine-judge constitution bench is considering whether privacy is a fundamental right of every citizen in a case that could have implications for Aadhaar.
It was not just about Aadhaar, the court said repeatedly, adding: "Don't forget the right to privacy of the little man."
The government put up a strong defence of the Aadhaar programme which, it said, had been praised by the World Bank and held up as an example for developing countries.
"We can't say every encroachment of privacy is to be elevated to a fundamental right. The claim to liberty has to subordinate itself to right to life of others," said Mr Venugopal.
Activists, lawyers and politicians have challenged the legal basis of Aadhaar. Four states - Congress ruled Karnataka, Punjab and Puducherry, and Trinamool-led Bengal - have joined the petitioners against the centre.
"Privacy, not being an absolute right, will never be. But a balance has to be maintained," said senior lawyer Kapil Sibal, representing the states.
During arguments so far, some judges have questioned how privacy could be enforced as a fundamental right when Google and Facebook extensively collect user data. "When one can share personal data with private players like Apple, why not share it with the government? What's the difference?" Justice DY Chandrachud has questioned.