Thousands took to the streets of Kolkata early Thursday morning to condemn the rape and murder of a medic that has triggered protests across India demanding better safety for women.

The discovery of the 31-year-old's brutalised body last week at a state-run hospital has sparked widespread outrage, 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."

Doctors in government hospitals across several states on Monday halted elective services "indefinitely", demanding speedy justice and better workplace security.

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

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 behaviour against women should be severely and quickly punished," he added.

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