"The rest of the four rapists should be hanged at the earliest. We have been battling for justice for three long years," said Badri Singh Pandey, the victim's father.
He said they will launch a nation-wide agitation on January 29 if the convicts were not awarded death sentence.
Asha Devi, the mother of the victim, demanded that fast-track courts be set up at all courts to offer speedy justice to sexual assault victims and that the Nirbhaya Fund be utilised for setting up state-of-the-art forensic labs in all states.
Their 23-year-old daughter, a paramedical student, died on December 29, 2012, at a hospital in Singapore.
The death sentence to four of the six rapists has been stayed by Supreme Court following an appeal challenging the high court order upholding the same.
Of the six rapists, while one committed suicide, another convict, a juvenile at the time of the crime, was recently released after spending three years at a correctional home.