NEW DELHI — Protests started across India Saturday to mark the death in a Singapore hospital of a woman beaten and gang raped in New Delhi. Prime Minister Manmohan Singh led appeals for calm.

Television channels showed crowds chanting and shouting slogans and heckling Delhi Chief Minister Sheila Dikshit near parliament in the Indian capital. The protest, in an area set aside by police, remained peaceful. News broadcasts showed demonstrations in Mumbai, Bangalore and Kolkata.

Delhi police will press murder charges against the six men accused of raping the woman and assaulting her with iron bars in the back of the bus on Dec. 16, spokesman Rajan Bhagat said by phone. The men may appear in court to be charged as soon as Jan. 3, he said.

The 23-year-old woman, who was raped in a moving bus, “passed away peacefully,” with her family and officials from the High Commission of India at her side, according to a statement from Kelvin Loh, chief executive officer at Mount Elizabeth Hospital. She had suffered “serious injuries to her body and brain,” he said. Air India has sent a plane to bring back her body, said G. Prasada Rao, a spokesman for the carrier.

Police barricaded roads in New Delhi and closed 10 subway stations amid calls for the death penalty for the six. Protests have been barred in the capital except at the designated site, Rajan Bhagat, a spokesman for the police, said in televised comments.

Constructive Action

“We have already seen the emotions and energies this incident has generated,” Singh said in an e-mailed statement. “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,” he said. It’s up to all Indians to “ensure that her death will not have been in vain.”

Singh has appointed a retired Delhi High Court judge to investigate the crime and fix lapses in policing. He also pledged to consider tougher penalties for sex crimes after the assault prompted street demonstrations organized through social-media postings.

The protesters, who fought water cannons and tear gas on Dec. 22 and Dec. 23, demanded more be done to protect women in the capital and across India.

“The need of the hour is a dispassionate debate and inquiry into the critical changes that are required in societal attitudes,” Singh said Saturday in his statement.

Unauthorized Bus

The increased public role of women “is accompanied by growing threats to their safety and security,” the prime minister said on Thursday. “We must reflect on this problem, which occurs in all states and regions of our country.”

After tricking the woman and her 28-year-old male friend into boarding the unauthorized chartered bus with dark, tinted windows and heavy curtains, the crew of the vehicle and accomplices assaulted the two over a period of about 45 minutes, stripped them and then threw them out.

The woman, a physiotherapy student, whose name can’t be revealed under Indian laws, was flown to Singapore for specialist treatment, paid for by the Indian government.

Data provided by India’s National Crime Records Bureau show about 24,200 cases of rape and 228,650 cases of crimes against women were reported in 2011.

United Nations figures show 1.8 cases of rape for every 100,000 in India, compared with 63 in Sweden, 29 in the U.K. and 27 in the U.S. Most instances of rape go unreported in India.

Singh has vowed to hasten prosecution of the accused. The panel led by the retired judge has been asked to rewrite criminal codes to allow harsher penalties to be imposed,harsher penalties, including capital punishment in the “rarest of rare” rape cases.

Courts Overburdened

It typically takes years for ordinary Indians to get justice because of a slow-moving legal process and overburdened courts. Long-running trials and lax enforcement of laws have also fueled protests in the nation’s capital.

About 63,342 cases were pending in the Supreme Court as of July 31, of which 67 percent have been on the roll for more than a year, government data show.

Before last month’s execution of Mohammed Ajmal Kasab, the lone surviving Pakistani gunman involved in the 2008 Mumbai attacks, India last carried out the death penalty in 2004, when a convict was hanged 14 years after he raped and murdered a school girl.

India has about 15 judges for each million of its 1.2 billion people, according to U.N. data. In China, there are about 159 judges for each million people, while in the U.S. the figure is about 108.