Fearing massive protests following the death, police tightened security in the capital and barricaded some sites of previous rallies.
Authorities said demonstrations are only allowed at Jantar Mantar observatory and the Ram Lila grounds.
Police banned protests in Raisina Hills and closed roads leading to the area, fearing a possible repeat of the furious, large-scale demonstrations that occurred last weekend. Ten metro stations also were ordered closed, authorities said.
Additional protests were planned Sunday in several cities, activists told CNN affiliate IBN.
Prime Minister Manmohan Singh offered his "deepest condolences."
"We have already seen the emotions and energies this incident has generated," he said, referring to the widespread protests. "It would be a true homage to her memory if we are able to channel ... these emotions and energies into a constructive course of action."
Reported rape cases in India -- where a cultural stigma keeps many victims from reporting the crime -- have increased drastically over the past four decades, from 2,487 in 1971 to 24,206 in 2011, according to official figures.
New Delhi alone had 572 rapes reported last year and more than 600 in 2012.
One such recent case involved a 17-year-old girl who said she was gang-raped during the Hindu festival of Diwali on November 13. A formal case wasn't registered by police until 14 days later.
The girl committed suicide Wednesday by ingesting poison, according to authorities in the Patiala district of Punjab, in northern India.
In her suicide note, she blamed her alleged rapists. Three suspects -- including a female accomplice -- have been arrested.
Most women in India have stories of sexual harassment and abuse on public transportation, on the streets and elsewhere, said Seema Sirohi of the Indian Council on Global Relations.
"There are a lot of reasons why this happens, but the patriarchal system is one, a lack of policing is another and general treatment of women is not equal to men, even though it may be so under the law," Sirohi said.
Human Rights Watch said the gang rape highlights the widespread problem of sexual violence in India.
"The government needs to act now to prevent sexual assault, aggressively investigate and prosecute perpetrators, and ensure the dignified treatment of survivors," said Meenakshi Ganguly, South Asia director for the organization.
The Indian government announced plans Thursday to "name and shame" convicted rapists by posting their names, images and addresses on official websites, according to the Times of India.
And the Cabinet plans to set up a commission to look into rape cases and suggest measures to improve women's safety. This group has three months to submit its report to the government.