The NRC is meant to identify original residents of Assam in an attempt to check illegal migration.
The top court said no agency or authority can make a statement like this while monitoring the process of publication of the draft NRC by an apex court appointed committee.
"We don't appreciate any other authority intervening in the matter of preparation and publication of the draft NRC when this court has been monitoring the process," the bench comprising Justices Ranjan Gogoi and RF Nariman said.
During the hearing the bench was informed that though the deadline for the publication of draft NRC was said to be March 31, 2019, the Chief Minister has stated that this would be done on or before December 2017.
"Last time you had told us that you will do it by March 2018. It is good that you are doing it. But we have an on-record statement of Chief Minister of Assam that the draft NRC will be published in December 2017. Let him supervise then. We will wash off our hands."
"When the Supreme Court is monitoring it, we don't see any other agency or authority to say that we will do it like this," the bench said.
It also said that the apex court has already spent its energy and time for almost two years and "it is not fair to the court".
The apex court had earlier asked for the preparation of NRC to keep a check on illegal migration from Bangladesh.
The apex court was hearing a matter relating to the fencing of an Indo-Bangla border.