The 32-year-old convict, submitted the plea last week. His mercy plea was dismissed by the President on January 17.
A bench headed by Chief Justice S.A. Bobde and comprising Justices B.R. Gavai and Surya Kant said: "If somebody is going to be hanged, then nothing can be more urgent than this."
Later in the day, the mentioning officer considered the urgency of Mukesh Singh's plea and listed it before a three-judge bench comprising Justices R. Bhanumathi, Ashok Bhushan and A.S. Bopanna.
The court had asked his counsel to approach the mentioning officer as the hanging is scheduled on February 1.
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Mukesh Singh had moved the mercy petition before the President after the apex court had dismissed his curative petition against his conviction and death sentence. The court had also dismissed the curative petition of another death row convict, Akshay Thakur.
Besides Mukesh, three others - Akshay, Vinay, and Pawan are facing the gallows for gang-raping a 23-year-old woman on the night of December 16, 2012, in a moving bus in the national capital.
Another accused, Ram Singh, allegedly committed suicide in Tihar Jail in March 2013 during the trial.
Another convict, who was a minor at the time of the crime, was sent to a reform facility and released after three years of the crime.
(with inputs from agencies)