Thousands of women marched across several Indian cities overnight and Prime Minister Narendra Modi called for strict punishment for crimes against women, as outrage and protests against the gruesome rape and murder of a doctor escalated.

Holding candles and posters that said "reclaim the night", women held marches across cities, including the eastern Indian city of Kolkata, where the rape and murder of a trainee doctor last week has triggered protests by fellow medics, demanding better and safer working conditions.

Many government hospitals in cities across India suspended all services except emergency departments earlier this week, as junior doctors sat outside in protest, demanding justice for the victim.

The 31-year-old doctor was found dead on Friday. Police said she had been raped and murdered and a police volunteer was subsequently arrested in connection with the crime.

"As a society, we have to think about the atrocities being committed against our mothers, daughters and sisters. There is outrage against this in the country. I can feel this outrage," Modi said in an address to the nation on its 78th Independence Day on Thursday.

The rape has revived memories of a similar case in New Delhi in 2012, when a gang of men raped and severely injured a 23-year-old student in a moving Delhi bus, leading eventually to her death.

"This horrific incident has once again reminded us that women disproportionately bear the weight of ensuring their own safety," Bollywood actor Alia Bhatt said in a post on her Instagram page, which has more than 85 million followers.

Doctors in India's crowded and often squalid government hospitals have long complained of being overworked and underpaid, and say not enough is done to curb violence levelled at them by people angered over the medical care on offer.

Crimes against women in India rose 4% in 2022 from the previous year, data from the National Crime Records Bureau (NCRB), released late last year, showed.