Deeply saddened by the death of the girl, he joined the nation in conveying to her family and friends his deepest condolences at this terrible loss.
"I want to tell them and the nation that while she may have lost her battle for life, it is up to us all to ensure that her death will not not have been in vain.
"We have already seen the emotions and energies this incident has generated. These are perfectly understandable reactions from a young India and an India that genuinely desires change. It would be a true homage to her memory if we are able to channelise these emotions and energies into a constructive course of action," he said in his condolence message.
He said the need of the hour is a dispassionate debate and inquiry into the critical changes that are required in societal attitudes.
Government, Singh said, was examining on priority basis the penal provisions that exist for such crimes and measures to enhance the safety and security of women.
"I hope that the entire political class and civil society will set aside narrow sectional interests and agenda to help us all reach the end that we all desire making India a demonstrably better and safe place for women to live in," Singh said in his condolence message.
The Prime Minister said he prays for the peace of the departed soul and hoped that her family will have the strength to bear this grievous loss.