India's prime minister called for calm Sunday after clashes erupted between police and demonstrators protesting a gang rape in the country's capital.

"We will make all possible efforts to ensure security and safety to all women in this country," Prime Minister Manmohan Singh said. "I appeal to all concerned citizens to maintain peace and calm."

Public outrage has surged after the gang rape and beating of a 23-year-old woman on a moving bus on December 16.

The prime minister's comments came after thousands of protesters defied a ban on demonstrations in New Delhi on Sunday.

For a second day, demonstrators were blasted with water cannons. While some dispersed, others huddled tightly in a circle to brave high-pressure streams in the cold December weather.

"We want justice!" the protesters shouted in chorus.

In addition to banners and cardboard placards, many demonstrators carried Indian flags as they scuffled with police. Authorities fired tear gas to try to break up crowds.

Police spokesman Rajan Bhagat said "hooligans who had joined the protesters" hurled stones, injuring 78 officers.

At least 65 protesters were also injured, he said.

Many police vans and a dozen public buses were damaged during the demonstrations, he said.

As he appealed for peace Sunday, Singh acknowledged that the anger is "genuine and justified."

Authorities haven't released the name of the rape victim, but protesters are calling her "Damini," which means "lightning" in Hindi.

"Damini" is also a 1993 Bollywood film whose lead female character fights for a housemaid, a victim of a sexual assault.

"We support you Damini. We'll keep fighting for you," a middle-aged woman at the historic India Gate said Sunday.

"Damini wants justice," read a placard at the protest.

Police bundled scores of young protesters into buses in the Raisina Hill area, home of the India Gate, the presidential palace, the parliament building and ministerial offices.

Demonstrators slipped under police vans to deflate tires and prevent them from driving off. Officers dragged them out.

The rape victim's injuries were so severe she spent days in intensive care in a city hospital, battling for her life. Police said Saturday that she had recovered enough to give a statement to a magistrate from her hospital bed the night before.

The protest was among a number of anti-rape demonstrations held across the country in the past week.

A video journalist was killed by police gunfire Sunday during a violent protest in India's remote northeastern state of Manipur, authorities said.

The journalist was covering a protest against a separate molestation case in the provincial capital of Imphal, state police said. Protests have rocked Manipur over the alleged molestation of a local actress by a suspected militant on December 18, during a public performance.

Protesters had torched a vehicle, forcing police to open fire, officer Manik Longjam said Sunday.

The journalist died in the gunfire, Longjam said.

Police said the molester was still at large.

Official data show that reported rape cases have increased more than tenfold over the past 40 years -- from 2,487 in 1971 to 24,206 in 2011.