Police in riot gear used tear gas and batons to hold crowds back from marching on the presidential palace, just as they did the day before in clashes that media reports said injured more than two dozen protesters.
Doctors said the 23-year-old victim of last week's attack, who was beaten, raped for almost an hour and thrown out of a moving bus in New Delhi, was still in a critical condition on respiratory support but responding to treatment.
New Delhi has the highest number of sex crimes among India's major cities, with a rape reported on average every 18 hours, according to police figures.
Most sexual assaults go unreported and unremarked, but the brutality of last week's attack triggered the biggest protests in the capital since mid-2011 demonstrations against corruption that rocked the government of Prime Minister Manmohan Singh.
The protesters, predominantly college students but also housewives and even children, are demanding more steps from the authorities to ensure safety for women and some want the death penalty for the accused.
Several city metro stations were closed and several roads were barricaded on Sunday to prevent a build-up of protesters.
However, by early afternoon the crowd around the India Gate monument normally a festive place on a Sunday - had swelled to more than 2,000, according to police there. Scuffles broke out near government buildings, where youths shouted "Down with Delhi police!" and threw bottles at the forces holding them back.
Bowing to public pressure, Sonia Gandhi, chief of the ruling Congress party, emerged from her residence after midnight to talk to protesters. She went out again on Sunday with her son, Rahul Gandhi, who is seen as a future prime minister.
"She assured us of justice," said one of the students who met the Gandhis, though some in the crowds shouted "Down with Sonia Gandhi!".
Since last week's rape, the authorities have promised better police patrolling to ensure safety for women returning from work and entertainment districts, the installation of GPS on public transport vehicles, more buses at night, and fast-track courts for swift verdicts on cases of rape and sexual assault.
Center>Copyright Reuters, 2012