The top court has asked the Central Government to file response within the next four weeks.
It has also put telecom service provider companies on notice.
Earlier in the day, the apex court rejected West Bengal Chief Minister Mamata Banerjee's plea over the issue, stating that she cannot challenge the Centre's order as a state government and asked her to file fresh petition as an individual.
Aadhaar has been in the center of "controversy" ever since its establishment with many incidents, of people dying due to denying of food grains and release of personal information on the internet, surfacing.
An 11-year-old girl allegedly died of starvation in Jharkhand's Simdega District recently as her family's ration card was not linked to the Aadhaar, the 12 digit unique-identity number issued to all Indian residents based on their biometric and demographic data.
The girl died on September 28 after her mother was unable to feed her.
The family was struck off from government welfare rolls for not linking their ration card with the Aadhaar card.
"Went to get rice, but I was told that no ration will be given to me. My daughter died saying 'Bhat-bhat' (rice)," said the girl's mother, Koyli Devi.
The state of Jharkhand is regarded as being among the poorest in India.
It is being alleged that millions of people in the state have been struck off the ration card rolls because they are not Aadhaar linked. (ANI)