Talking to reporters, the protesters quoted her as saying that the government was taking serious note of their demands.
"She said the law and order situation will change very soon and the victim will get justice very soon," one of the protesters who met Gandhi told the media.
"She said sections 307 and 201 (of Indian Penal Code) will be added to the charges against the accused."
Section 307 relates to attempt to murder and 201 pertains to causing disappearance of evidence of offence or giving false information.
The protesters refused to give their names to the media, saying they were members of the "common public". They, however, added that the protests sweeping the city centre would continue.
Congress general secretary Rahul Gandhi, Minister of State for Home RPN Singh and party leader Renuka Chowdhary were present at the meeting.
This was the second time Sonia Gandhi met a section of young men and women who have been protesting noisily against December 16 rape that left the victim battling for life in hospital.
Gandhi came out of her residence past midnight and assured the protesters that "justice will be delivered".
According to one who was present, she spent about 20 minutes with 40-50 students and said she was "with them".
On Sunday morning, according to some students, she met a few women protesters and assured them her support.
On Saturday, thousands tried to enter Raisina Hill, which leads to the presidential palace. Police used batons and tear gas and sprayed water to disperse the crowds.
New Delhi: Congress president Sonia Gandhi on Sunday promised a group of young protesters that speedy action would be taken against those who brutally raped a 23-year-old woman in a moving bus.
First Published: Sunday, December 23, 2012, 13:24