The apex court said the death row convicts had failed to point out "error apparent on the face of record" in the verdict. The highest court of India has rejected their plea and has upheld the hang to death verdict.
She said it had been a hard battle - but nothing compared to the 14 days she spent by her daughter's side as she fought and lost the battle for her life, reports the BBC's Divya Arya, who was at court.
The convicts have the option of seeking presidential commutation of their death sentences which seems unlikely given the severity of the crime and the views of the trial court, HC and the SC. The remaining four accused were sentenced to death by Additional Sessions Judge.
Delhi Commission for Women (DCW) Chairperson Swati Maliwal also welcomed the development even as she questioned the six-year delay in dispensing justice in the case.
More than 370 convicts were on death row as on December 2017, the last official count, down from 399 the previous year.
Asha Devi, mother of the gang-rape victim, addressing the media at the Supreme Court after the verdict on Monday.
India has long exercised the death penalty as punishment for serious crimes; its last execution was in 2015 of Yakub Memon for his role in the 1993 terrorist bombings in Mumbai.
She, however, added, "As far as death penalty is concerned, as a matter of principle, we are against it". The culprits arrested were Mukesh, Pawan Gupta, Vinay Sharma, Ram Singh and another young man who was just short of his 18th birthday. "Hope government will now follow up to act decisively on issues of women's safety (sic)", Randeep Surjewala, the chief spokesperson of the party, wrote on Twitter.
The brutality of the crime had led to nationwide street protests and changes in laws regarding sexual violence against women.
A juvenile, who was among the accused, was convicted by a juvenile justice board.
On May 5 previous year, the top court had upheld the death penalty to the four convicts - Mukesh (29), Pawan (22), Vinay Sharma (23) and Akshay Kumar Singh (31), saying the "brutal, barbaric and diabolic nature" of the crime could create a "tsunami of shock" to destroy a civilised society.
The nation went into shock as twenty three year old Nirbhaya was gang raped, tortured and killed in a moving bus.
Five men and a juvenile had lured the 23-year-old trainee physiotherapist and her male friend on to a bus in New Delhi on December 16, 2012, before repeatedly raping the woman and beating both with a metal bar and dumping them on a road.