The director of a controversial documentary about the fatal gang rape of a young woman in Delhi has branded a ban on the film being shown in India as “misguided”, accusing her critics of reacting “hysterically”.

India’s Daughter, made by Leslee Udwin, triggered national debate in India with the government banning the film “across all media platforms” and attempting unsuccessfully to stop it being broadcast anywhere in the world. Udwin, facing a criminal charge of intent to breach the peace, left India last Wednesday, on the advice of her lawyers, fearing for her safety. The documentary – based on the brutal rape and murder in 2012 of medical student Jyoti Singh, 23 – will be shown simultaneously on channels in six countries, including BBC4, on Sunday as part of International Women’s Day.

The film has had an extraordinary response on social media – more than 32 million hits, according to Udwin – first triggered by an interview with the director in last Sunday’s Observer.

Udwin, who has appealed to India’s prime minister, Narendra Modi, told the Observer: “Banning the film is so misguided, how can you tell other countries how they should interpret free speech? The impetus was a genuine love of India. Women and men across the country went on the streets for a month demonstrating for women’s rights following the rape. This was my ‘thank you’ for defending my rights. So many of the critics haven’t even seen the film yet they have reacted hysterically to their own inaccuracies not the facts.

“On International Women’s Day, symbolically, we should be holding hands across the world to bring about change, not fighting such an undemocratic action.” Udwin, her husband, Kim, an actor, and her children, Maya, 15, and Emil, 18, fly to New York on Sunday for a screening of the film on Monday and the launch of the India’s Daughter campaign, tackling global gender inequality and violence against women. “We are all going to New York as a treat because the family lost their mother for two years while I made the film,” Udwin said.

The campaign is supported by actresses Freida Pinto, Emma Thompson, Anne Hathaway and Meryl Streep among others, as well as a number of organisations including the charity Plan in the UK which focuses on girls’ rights globally and for whom Udwin is an ambassador. The Israeli-British director added: “Critics have taken such a narrow view of the film. It isn’t about India alone. It’s about the scale of global violence against women.”

In the documentary, one of the convicted rapists, Mukesh Singh, who drove the bus as Jyoti Singh was raped, beaten and eviscerated, blamed her for the crime. “A decent girl won’t roam around at nine o’clock at night,” he said, showing no remorse. “A girl is far more responsible for rape than a boy.” The two defence lawyers, ML Sharma and AK Singh, also make misogynistic comments. Sharma says: “In our culture, there is no place for a woman.”

On Wednesday, the Indian parliament erupted over the issue of the documentary. Rajnam Singh, the home minister, who called for the ban, said he was “shocked” and “hurt”. A member of parliament, Ranjeet Ranjan, said the documentary was “humiliating for women” and criticised “the commercialisation of rape”.

She was countered by Javed Akhtar, who welcomed the documentary, saying: “Scores of men in India have come to know that they think like a rapist.”

Last Thursday in the north-east state of Nagaland in India, a man accused of rape was dragged from prison by a mob and beaten to death.