There is growing anger in India over the gang rape and murder of a 27-year-old woman on the outskirts of Hyderabad.

Police have arrested four men over the death of the woman, a veterinarian, whose charred body was found some 30km away from the toll booth where she last spoke on the phone to her sister.

The case has led to the suspension of ordinary business in both India’s houses of parliament on Monday as MPs debated the state of women’s safety in the country.

And the chief minister of Telangana, the state where the attack took place, has been criticised for responding by suggesting female workers should be subject to a curfew for their own protection.

An initial police report says the veterinarian, who as a victim of sexual assault cannot be named for legal reasons, was travelling last Wednesday evening for a doctor’s appointment when she suffered a flat tyre.

She called her family to say she was stranded at a toll booth and that a lorry driver had offered to help her, after which she became uncontactable.

Police say they believe the four men had punctured her tyres and then pretended to offer their assistance. After taking her scooter on the pretence of getting it fixed, they dragged her away from the main road, sexually assaulted and then killed her, before dumping the body in another town and setting it on fire, it is claimed.

The case is reminiscent of the high-profile gang-rape and murder of a young woman on board a bus in Delhi in 2012, which sparked a tightening of the laws around sexual assault.

The veterinarian’s name, despite reporting restrictions that are enforced in India even after the victim’s death, was one of the top trends on Twitter throughout the weekend.

On Saturday, thousands of protesters gathered outside a police station in Hyderabad demanding the four suspects be handed over to them, and at one point clashed with officers. Smaller protests have also taken place in Delhi, with activists carrying placards demanding justice and an end to violence against women.

Speaking in the upper house of parliament on Monday, the opposition Samajwadi Party leader Jaya Bachchan said a “similar” rape case was reported in Hyderabad the day before the attack on the vet, and questioned why police were unable to keep people safe in the city.

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“I think these people need to be shamed in front of the entire country,” she said. As for those accused of committing the crime, she said that “these kind of people should be brought out in public and lynched”.

Rajnath Singh, the defence minister, said the government was ready for a discussion on crimes against women and whether legal protections could be strengthened further.

Of the Hyderabad case, he said: “This act has brought shame to the entire country. It has hurt everyone. The accused must be given the most stringent punishment for their crime.”

Most political leaders have commented on the case in recent days, although Narendra Modi, the prime minister, is yet to give his reaction.

Priyanka Gandhi Vadra, of the main opposition Congress party, said she had been “deeply disturbed”. “As a society, we have to do far more than just speak up when these horrific incidents take place,” she said.

Telangana’s chief minister, K Chandrashekar Rao, said the suspects would be tried in the fast-track courts system, set up in 2000 and given a new injection of funding specifically to deal quickly with rape cases after the 2012 Delhi bus attack.

But he sparked controversy with comments on Sunday at an event for employees of the state transport body, suggesting women should not be working at night as a safety measure.

Rekha Sharma, chair of the National Commission for Women, said she was “shocked to hear [Mr Rao] saying women should be home by 8pm”.