"How can state file such a plea?"
The Union government will now have to submit its reply within four weeks.
Banerjee last week had said that she would not comply with the mandate and refused to link her mobile connection with Aadhaar, even if that meant she would lose her phone service.
But, on October 25, the Centre indicated that the deadline for linking Aadhaar with bank accounts, mobile numbers and other schemes for those who don't have the number and are willing to go for it, may be extended till March 31.
"In a federal structure, how can a state file a plea challenging Parliament's mandate?" the apex court asked.
On 24 August, in a path-breaking ruling, the apex court held that privacy is a fundamental right under the Constitution of India.
Venugopal said on Monday the Centre had prepared an affidavit outlining the uses of Aadhaar and how the government is working towards implementing the scheme without any glitches.
In August a Punjab government website had exposed the Aadhaar numbers of over 20,000 people who had applied for low-priced housing in Ludhiana and Jagraon. Earlier, the deadline for linking of Aadhaar was December end this year.
However, Mr. Venugopal had agreed to take instructions on certain issues on Aadhaar after which the court had asked him to mention the matter again on October 30. The court, however, asked the West Bengal counsel to amend its prayer and submit a fresh plea.
However, while the top court dismissed the West Bengal government's writ petition, Justice AK Sikri also noted that chief minister Mamata Banerjee can file a petition on the issue as an individual citizen.
A separate petition challenging a notification of the Department of Telecom (DoT) for mandatory linking of mobile numbers with Aadhaar has also been filed in the court and is likely to come up for hearing today.