Protests against sexual violence are spreading across south Asia as anger following the gang rape and death of a 23-year-old medical student in Delhi courses through the region.

Inspired by the rallies and marches staged across India for nearly three weeks, demonstrations have also been held in Nepal, Sri Lanka, Pakistan and Bangladesh – all countries where activists say women suffer high levels of sexual and domestic violence.

In Nepal, the case of a 21-year-old woman who says she was raped and threatened with death by a police officer and robbed by immigration officials, prompted hundreds of demonstrators to converge on the prime minister's residence in Kathmandu. They called for legal reforms and an overhaul of attitudes to women.

"We had seen the power of the mass campaign in Delhi's rape case. It is a pure people's movement," said Anita Thapa, one of the demonstrators.

Bandana Rana, a veteran Nepalese activist, described the ongoing protests in Delhi as "eye-opening". "A few years back, women even talking about sexual violence or even domestic violence was a very rare," she said.

Sultana Kamal, of the Bangladeshi human rights group Ain o Salish Kendra (ASK), said the protests in Delhi had given fresh impetus to protests against sexual violence.

One incident that has provoked anger in Bangladesh was the alleged gang rape of a teenager by four men over four days in early December in Tangail, 40 miles north-west of Dhaka. The men were said to have made videos of the attack before leaving their victim near a rail track where she was eventually found by her brother.

On Friday a teenager who was said to have been repeatedly raped in a hotel died in hospital in Dhaka of injuries sustained when she subsequently tried to take her own life.

But despite the widespread anger, the social stigma attached to rape victims remains a major problem throughout the region.

Although Bangladesh police arrested suspects in both the cases and investigations are under way, activists fear that corruption as well as deep-seated misogyny among investigating officers and the judiciary make convictions unlikely.

According to ASK's statistics, at least 1,008 women were raped in 2012 in Bangladesh, of whom 98 were later killed.

Khushi Kabir, one of the organisers of a "human chain" in Dhaka to protest against violence to women, said its aim was "to show that people are not going to just let this [movement] die down".

Kabir said although previous demonstrations on similar issues were largely dominated by women, men were now protesting too. The protests had also drawn people from a broad range of society. "We had lawyers, schoolchildren, teachers, theatre activists and personalities, industrialists," she said.

One week after the Delhi rape victim died in a Singapore hospital, the widespread grief and outrage have moderated, but a fierce debate still rages over the country's sexual violence and attitudes to women. One politician from the opposition BJP party was forced to apologise after stating the women who did not stay "within moral limits … paid the price". A senior official in a hardline Hindu nationalist volunteer organisation provoked controversy when he claimed that westernisation was responsible for rapes in cities.

The Delhi rape case is being heard in a special fast-track court inaugurated last week to deal with such offences in the capital. A hearing in the case is scheduled for Saturday. Protests however continue, albeit at a lower intensity than in previous weeks.

The Indian media continue to give prominence to news items that would barely have received attention a month ago.

On Friday it was reported that a 19-year-old woman had died in a hospital in the north-western city of Jaipur after she set herself on fire allegedly following aggressive harassment from a neighbour. She said the man had threatened to kill her brother and father if she did not marry him.

In another incident reported on Friday a woman was said to have jumped from a moving train to escape an assault. Sexual harassment on public transport is endemic in India where men target single young women. Such abuse is described euphemistically as "eve-teasing" with perpetrators dubbed "railway Romeos".

One persistent problem, women say, is men filming their faces or bodies on mobile phones in buses or trains.

Indian activists have repeatedly argued that media descriptions of such activities as "eve-teasing" contribute to the widespread acceptance of sexual harassment in public places.

A recent survey by the Hindustan Times newspaper found that nearly 80% of women aged between 18 and 25 in Delhi had been harassed last year and more than 90% of men of the same age had "friends who had made passes at women in public places". Nearly two-thirds of the latter thought the problem was exaggerated. It was also reported on Friday that though Delhi police had received 64 calls alleging a rape and 501 calls about harassment since 16 December, only four formal inquiries had been launched.

Senior officials across the south Asian region have defended their government's records on tackling sexual violence against women. In Delhi, Sushilkumar Shinde, the Indian home secretary, said on Friday that crimes against women and marginalised sections of society were increasing, and it was the government's responsibility to stop them. "This needs to be curbed by an iron hand," he told a conference of state officials from across India convened to discuss how to protect women. He called for changes in the law and the way police investigate cases so justice could be swiftly delivered. Many rape cases are bogged down in India's overburdened and sluggish court system for years. "We need a reappraisal of the entire system," he said.

Dr Shirin Sharmin Chowdhury, the Bangladeshi minister for women and children's affairs, said her government was "taking this issue very seriously".

"Just yesterday [Thursday] a sex offender … was given a very high punishment under the law," she said, "but sometimes the delay and the whole process of the trial takes a bit of time to ensure justice."

Protests are expected on Saturday in Bangladesh following the news of a new incident: the rape and killing of a student in the south-east of the country. The 14-year-old is reported to have left home to bring in her family's cows in Rangamati district one evening earlier this week. Her uncle later found her body in a forest. An autopsy report later confirmed that she had been raped and then strangled.

• Additional reporting: Ishwar Rauniyar in Kathmandu, Saad Hammadi, Dhaka.