Manmohan Singh also expressed the hope that the entire political class and civil society will set aside narrow sectional interests and agenda to make India a demonstrably safer place to live in.
He said it would be a true homage to her memory if the emotions and energies of the youth generated by the brutal assault on her are channelised into a constructive course of action.
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.
President expressed his grief over the death of the girl
Describing the 23-year-old gangrape victim who died in Singapore as a "brave daughter of India", President Pranab Mukherjee today said all steps to bring the perpetrators of this "ghastly crime" to justice should be taken to ensure that her death will not be in vain.
"She was a brave and courageous girl who fought till the very last minute for her dignity and her life. She is a true hero and symbolises the best in Indian youth and women...The nation will mourn the passing of this brave daughter of India," the President said in his condolence message.
He appealed for peace and calm and called upon authorities to take all necessary steps to bring the perpetrators of this ghastly crime to justice.
"Deeply distressed" by the "unfortunate demise" of the girl, he said while conveying his condolences to her parents and family who have faced this adversity with "fortitude and grace" and prayed that they have the strength to bear this loss.
"At the same time, let us resolve that this death will not be in vain. We will do everything possible to ensure that such an incident never happens again," he said.
Vice President condoles the death of girl
Condoling the death, Vice President Hamid Ansari said, "I am profoundly saddened at the passing away of the young girl, rightly being referred to as India's daughter".
"A young, promising life has been brutally snatched away in most tragic circumstances. Not only has the family lost a daughter and a sister, every Indian is today feeling the sense of loss as we all had come to identify with the braveheart as she fought valiantly for her life," he said.
Ansari expressed hope that "this heart rending tragedy would compel us as people to focus on social norms and practices which are violative of human rights and an impediment to progress in the modern world."