"The three convicted persons should be hanged to death as the offence committed by them falls under the category of the rare of rarest," Additional Public Prosecutor Satwinder Kaur told the judge, who had held the trio guilty of the offences.
The prosecution further said that there is no chance of their reformation as the convicts -- Rahul (27), Ravi (23) and Vinod (23)-- have not shown any remorse during the trial of the case.
Accused had inserted a broken liquor bottle into victim's private parts.
However, the counsel for the accused said that they should be given chance to reform as there is full chance for mending.
The court, however, reserved its order on sentence for February 19, after the arguments on quantum of punishment were concluded from both sides.
Holding that the girl was killed in a cold blooded manner, Additional Sessions Judge Virender Bhat on February 13 had held the trio guilty of the offences and said they "gratified their sexual lust upon the deceased by subjecting her to rape one by one".
The three youths were arrested and booked for offences of kidnapping, unnatural sex, gangrape and murder of a girl on intervening night of February 9 and 10, 2012.
The court, however, had acquitted the three of the charges of unnatural sex saying no such evidence found against them.
According to the prosecution, the girl, who was working as a data entry operator in Gurgaon's Cyber City, was abducted by the three in a car near her house in Qutub Vihar here and was gangraped and murdered by them on February 9, 2012.
Kaur had informed the court that the victim's mutilated body was found three days after the incident from a field in Rodhai village in Haryana's Rewari district.
Kaur had said the three youths had poured acid into the victim's eyes and had inserted a broken liquor bottle into her private parts.
She had also said that Ravi and Rahul, who were residing in that area as tenants, were brothers and had planned to take revenge on the girl as she had rejected Ravi's advances.
The girl was kidnapped by the three youths when she along with three colleagues was coming back from her Gurgaon office, the prosecutor had said, adding they had dragged her into their car and had sped away.