Thousands took to the streets of Kolkata early Thursday to condemn the rape and murder of a local doctor, demanding justice for the victim and an end to the chronic issue of violence against women in Indian society.

The discovery of the 31-year-old's brutalized body last week at a state-run hospital has sparked nationwide protests, with Prime Minister Narendra Modi demanding swift punishment for those who commit "monstrous" deeds against women.

Large crowds marched through the streets of Kolkata in West Bengal to condemn the killing, with a candlelight rally at midnight coinciding with the start of India's Independence Day celebrations on Thursday.

The protesters in Kolkata, who marched under the slogan "reclaim the night," called for a wider tackling of violence against women and held up handwritten signs demanding action.

"We want justice," read one sign at the rally. "Hang the rapist, save the women," read another.

"The atrocities against women do not stop," midnight marcher Monalisa Guha told Kolkata's The Telegraph newspaper.

"We face harassment almost on a daily basis," another marcher, Sangeeta Halder, told the daily. "But not stepping out because of fear is not the solution."

'Anger in the nation'

Modi, speaking in New Delhi on Thursday morning at Independence Day celebrations, did not specifically reference the Kolkata murder, but expressed his "pain" at violence against women.

"There is anger for atrocities committed against our mothers and sisters, there is anger in the nation about that," he said.

"Crimes against women should be quickly investigated; monstrous behavior against women should be severely and quickly punished," he added.

"That is essential for creating deterrence and confidence in the society."

Doctors are also demanding swift justice and better workplace security in the wake of the killing, with those in government hospitals across several states on Monday halting elective services "indefinitely" in protest.

Protests have since occurred in several other hospitals across the country, including in the capital.

"Doctors nationwide are questioning what is so difficult about enacting a law for our security," Dhruv Chauhan, from the Indian Medical Association's Junior Doctors' Network, told the Press Trust of India news agency.

"The strike will continue until all demands are formally met."

The Telegraph on Thursday praised the "spirited public protests" across India.

"Hearteningly, doctors and medical organizations are not the only ones involved," it said in an editorial.

"The ranks of the protesters have been swelled by people from all walks of life."