Vinay Sharma has also asked the top court to reduce his punishment to life imprisonment.
One of the four death row convicts in the Nirbhaya case challenged the rejection of his mercy petition by President Ram Nath Kovind in the Supreme Court on Tuesday. Vinay Sharma's counsel, AP Singh, also sought the reduction of his punishment from death sentence to life imprisonment.
Vinay Sharma and three other accused -- Mukesh Kumar Singh, Pawan Gupta and Akshay Kumar - have been found guilty of brutally raping and murdering a 23-year-old paramedical student in Delhi on December 16, 2012.
President Ram Nath Kovind had rejected Vinay Sharma's plea for clemency on February 1. A day earlier, a trial court had stayed "until further orders" the execution of all the four convicts in the case.
Pawan Gupta is yet to file a curative petition, the last and final legal remedy available to a person sentenced to death. He also has the option of filing a mercy petition.
Although six people were originally found guilty, one of them -- a juvenile -- was let off after being made to serve in a correctional home for three years. The prime accused, Ram Singh, committed suicide by hanging himself in Tihar Jail days after the trial began.
The remaining four convicts were sentenced to death in September 2013 by the trial court.
Meanwhile, the parents of the rape victim have moved a Delhi court to seek the issuance of a fresh death warrant against the convicts, news agency PTI reported. They claimed that the convicts were making a "mockery of the law".
After hearing the plea, Additional Session Judge Dharmender Rana issued a notice to all the convicts and said it will take up the matter on Wednesday.
Mukesh Kumar Singh had earlier challenged the rejection of his mercy plea before the Supreme Court. His petition was rejected.
(With inputs from PTI)