The 23-year-old physiotherapy student was attacked on a bus as she and a male friend returned from watching a film in December 2012.
Delhi Police, however, opposed the review plea and told the court that submissions advanced by the counsel appearing for Mukesh do not make out a case for review of the apex court's judgment.
"Singh that death penalty has been abolished by the Parliament of United Kingdom in the year 1966 and several Latin American countries, and Australian states have also abolished death penalty, is no ground to efface death penalty from the statute book of our country", Justice Bhushan, writing the judgement for the bench, said while rejecting the review pleas filed by Vinay and Pawan.
On May 5 past year, the top court had upheld the death penalty to the four convicts.
A panel entrusted with reviewing legislation boosted the jail terms to 20 years for rape despite rejecting public appeals for the death penalty.
The court said the death-row convicts had failed to point out any "error" in the earlier judgment. Their sentence was upheld by the Delhi high court in 2014. The incident occurred in Delhi on December 16, 2012. They can file one last petition with the Supreme Court, and if it's again rejected, they can seek presidential mercy, said A.P. Singh, the defence attorney.
One of the accused in the case, Ram Singh, had allegedly committed suicide in the Tihar Jail. "The stringent measures taken by our government are working and will act as a strong deterrent for the perpetrators of such heinous crimes", she said. Of six assailants eventually arrested, the fifth man died in prison in 2013 and the sixth was a juvenile who served his three-year sentence in a youth offender facility. She came to be known as "Nirbhaya", meaning "fearless".
The six gang raped and tortured the woman with an iron bar as the bus drove loops through the Indian capital.
She was dumped on the streets after 45 minutes with horrific internal injuries, and died 13 days later in a Singapore hospital.
According to National Crime Records Bureau data for 2016, incidents of rape of children in India increased by over 82 percent compared with 2015, when almost 35,000 rape cases were reported to the police. On July 9, 2018 SC will decide the fate of the four accused of death sentence in the Nirbhaya gang-rape case.
More than 370 convicts were on death row as on December 2017, the last official count, down from 399 the previous year.