Mukesh, who has been sentenced to death along with three other convicts in the case, had filed the petition.
The apex court, in May, upheld the order of Delhi High Court, which had sentenced the four convicts - Akshay, Pawan, Vinay Sharma and Mukesh - to death.
On December 16, 2012, six people gangraped a 23-year-old physiotherapy intern in a moving bus in Delhi.
The woman succumbed to her injuries in a Singapore hospital on December 29, 2012.
One of the accused, Ram Singh, had hanged himself in the prison, while another person, who was a juvenile at the time of the crime, was convicted in August last year and is serving the maximum sentence of three years in a reform home. (ANI)