The petitions were filed by Vinay Sharma and Mukesh Kumar on Thursday last.
However, among the four convicts that had been issued death warrants, the rest of the two- Akshay Kumar Singh and Pawan Gupta- has not yet sought any kind of relief till now.
A curative petition is the last course of legal remedy available for a convict.
A bench comprising of Justices N V Ramana, Arun Mishra, R F Nariman, R Banumathi and Ashok Bhushan heard and dismissed the petitions of Sharma and Kumar.
The curative petitions were filed two days after a Delhi court issued death warrant for the four convicts.
The court had directed that the four convicts be hanged to death on January 22 at 7 am.
One of the convicts, Sharma had in his curative petition stated that he was only 19 years old when he committed the brutal crime.
He also stated in his plea that his young age, socio-economic factors were not considered and the court relied on factors such as collective conscience of society and public opinion in giving its judgement.
The four convicts were convicted for the brutal gang rape and murder of a 23-year-old paramedic student in a moving bus in New Delhi in December 16, 2012.
The student, who came to be known as Nirbhaya (fearless), died on December 29, 2012 at Mount Elizabeth Hospital in Singapore.
The Nirbhaya gang rape sparked widespread protests across the country and forced the government to set up a committee to review the country’s laws on rape and crime against women.
Based on the committee’s recommendations, the government amended rape laws to make them tougher.