An appeal on behalf of the condemned convicts, Vinay Sharma (21) and Akshay Kumar Singh (29) was filed while two others, Mukesh (27) and Pawan (20), had approached the apex court earlier and their execution has already been stayed.
The Delhi High Court had on March 13 this year upheld their conviction and award of the death penalty by terming the offence as "extremely fiendish" and "unparalleled in the history of criminal jurisprudence" and said the "exemplary punishment" was the need of the hour.
It had also said if this case was not "the rarest of rare cases" then "there is likely to be none".
Besides seeking setting aside of the High Court verdict, Vinay and Akshay, in their appeal filed through lawyer A P Singh, have sought a stay on their execution as an interim relief.
The petition said the judgement be set aside as there was no "substance or material piece of evidence" and there were contradictions in the depositions of the victim and her friend, who had accompanied her in the bus, about the offence and the offenders.
It said the testimony of the SDM cannot be relied on as she had deposed that the victim was "comfortable, happy and willing to record her statement."
"Whether a patient who is on ventillator...can be happy and comfortable," it said.
Disputing the veracity of the dying declaration of the victim, it said she was not fit enough to record her statement and hence, the statement made through gestures cannot be relied upon.
"The High Court failed to appreciate before awarding death sentence to appellant Vinay Sharma that he was juvenile at the time of the incident...," it said.
The 23-year-old paramedic, on the night of December 16, 2012, was brutally assaulted and gangraped by six persons in a moving bus in South Delhi and thrown out of the vehicle with her male friend. She later died in a Singapore hospital on December 29.