In a message on the eve of Christmas, the president expressed "anguish and distress" over the horrific attack on the 23-year-old girl in the national capital on December 16.
"We mark Christmas at a time when the nation is joined in anguish and distress over the recent horrific attack on a young girl in New Delhi," he said.
There have been wide spread protests across the city, including in front of Rashtrapati Bhavan over the weekend, with agitated youths demanding swift action against the perpetrators of the heinous crime.
"I laud the courage and tenacity of this young lady and her family. On this Christmas day, let us join in prayer for the full and speedy recovery of this strong and courageous girl," the President said.
The president, who devoted a significant portion of his customary message to the rape incident, which has outraged the nation, asked the countrymen to resolve to "redouble efforts" for the protection of women and their welfare.
"Let us strive to ensure that women feel safe and secure at all times in our country," he said.
"May the Christmas bells dispel hatred and violence. As the world lights candles for Christmas this year, may the spirit of caring and sharing pervade our beings," Mukherjee said.The president asked people to renew minds and hearts with the teachings of love and compassion of Jesus Christ and recalled his sacrifice for humanity.