The death of the girl, whose body was cremated in Delhi on Sunday morning, led to a massive outpouring of grief and anger across India.
Millions of Indians held candlelight vigils and protests demanding immediate action from the government to punish perpetrators of the heinous crime and strengthen laws that deal with violence against women.
Ban welcomed efforts of the Indian government to take urgent action in the case and called for "further steps and reforms to deter such crimes and bring perpetrators to justice," a statement issued on Saturday by the UN Secretary General's spokesperson said.
He also encouraged the Indian government to strengthen critical services for rape victims and said the UN Women and other agencies of the United Nations stand ready to support such reform efforts with technical expertise and other support as required.
The UN chief offered his sincerest condolences to the girl's parents, family and friends.
"Violence against women must never be accepted, never excused, never tolerated. Every girl and woman has the right to be respected, valued and protected," he added.