Outrage has continued to grow in India over the gang-rape and murder of a 27-year-old woman, with protesters taking to the streets and politicians calling for the offenders to be “lynched”.

Demonstrations spread to cities including Delhi, Bengaluru and Kolkata and MPs spoke out in parliament following the discovery last week of the woman’s burned body in Hyderabad.

Four men now in police custody are alleged to have deflated the vet’sscooter tyres in order to leave her stranded then approached her appearing to offer to help. It is alleged she was dragged to an abandoned area by the roadside where she was gang-raped, asphyxiated to death and her body set alight and dumped.

“This act has brought shame to the entire country, it has hurt everyone,” said the defence minister, Rajnath Singh, speaking out against what he called a “heinous crime”.

Violent crimes against women have been in the spotlight in India since 2012, when the fatal gang rape of a young woman aboard a moving bus in Delhi prompted hundreds of thousands to take to the streets to demand stricter rape laws.

Protesters on Monday demanded a fast-track investigation in the Hyderabad case, with anger mounting both on the streets and in parliament.

Jaya Bachchan, an MP and former Bollywood actor who has been a vocal proponent of women’s rights, was among those who spoke out. “I know it sounds harsh, but these kind of people should be brought out in public and lynched,” she said in parliament.

She demanded to know how the Indian government planned to improve safety for women in India and protect them against sexual violence. Last week multiple rapes and murders were reported, including the gang-rape and murder of a lawyer in Jharkhand and the rape and murder of a six-year-old child in Rajasthan.

“The people want the government to give a proper and definite answer,” said Bachchan.

Outrage over the 2012 Delhi rape prompted thousands of women to take to the streets and spurred quick action on legislation, doubling prison terms for rapists to 20 years and criminalising voyeurism, stalking and the trafficking of women. Indian MPs also voted to lower to 16 from 18 the age at which a person can be tried as an adult for heinous crimes.

Protesters on Monday demanded more stringent laws to protect women in India.

In the eastern city of Kolkata, where protests were held throughout the day, college student Bandana Mondal said it was becoming difficult to sit back and watch silently.

“It is time to hit the road and seek faster punishment for the offenders. The process of law appears slow and there is hardly any deterrent,” she said.

In Hyderabad, which has seen the largest of the protests, student activists linked to prime minister Narendra Modi’s ruling Bharatiya Janata Party asked for capital punishment. Police in the city had used force on Saturday to disperse hundreds of protesters after they tried to storm into a police station where the four accused were held.

At a demonstration in Delhi, student Aditi Purohit said that she was so angry and frustrated that she had left her classes and come out. “If they [the accused] were in front of me, I would have killed them,” she said

Sexual violence against women remains rife in India and it is the most dangerous place in the world to be a woman, according to a 2018 survey by the Thomson Reuters Foundation.

People stand on police barricades as they hold placards and shout slogans during a protest in Dehli. Photograph: Danish Siddiqui/Reuters

Campaigners say the government has failed in checking the rising crimes against women. Jyoti Badekar, a womens rights activist from Mumbai, said the lack of female police staff is one of the factors fuelling the problem.

Police in the country registered 33,658 cases of rape in 2017, according to the most recent available official records – an average of 92 a day - but the real figure is believed to be far higher as many women in India do not go to the police out of fear.

Tens of thousands of cases also remain stuck in courts, often hindering victims and their families as they navigate the slow and cumbersome legal system. Figures for 2017 reveal that courts opened 18,300 cases related to rape but more than 127,800 more remained pending at the end of the year.

“It’s very frustrating for the victim. You keep on going to court, and even after evidence is over, they take a long time to pass the judgement,” women’s rights lawyer Flavia Agnes told Reuters.