Ms Batty, a leading campaigner against domestic violence, made the remarks in a letter sent to Mr Turnbull on Thursday by Researchers Against Pacific Black Sites, a group of academics concerned by human rights abuses in the centres. Rosie Batty with Prime Minister Malcolm Turnbull and Minister for Women Michaelia Cash. Credit:Eddie Jim It comes amid harrowing tales of rape and sexual abuse of women on Nauru, including the airing of a distressing phone call from a young Somali woman to Nauru police after being allegedly raped by a group of men. It took the police four hours to attend to her, ABC's 7.30 program reported on Monday. At least two other women have also been raped or assaulted on the island, including Nazanin, an Iranian woman who was repatriated to Australia for treatment three months after the incident, but only after a public campaign and after twice attempting suicide and suffering organ failure when she stopped eating.

Mr Turnbull on Thursday said the reports were "very alarming". But, while saying the government was improving safety and security and helping Nauruan police establish a gender violence unit, he remained steadfast that the detention centres would remain in place as they deterred asylum seekers taking the risky journey by sea to Australia. "The one thing we know is these policies, tough though they are, harsh though they are in many respects, actually do work, they save lives," the Prime Minister said. The letter is part of the "Out of Sight NOT Out of Mind" campaign led by Researchers Against Pacific Black Sites that aims for domestic violence organisation to expand their advocacy to the "torture" that is taking place in offshore detention centres. Ms Batty says: "Those of us who care about violence against women, children and other vulnerable people at home need to care about what happens to these same people elsewhere who are under our care.

"The Australian government funds the offshore detention centres on Nauru and Manus Island. The centres are, by their very design, unsafe and dangerous places." Last week, Ms Batty stood alongside Mr Turnbull and Minister for Women Michaelia Cash to announce new funding to counter domestic violence. Mr Turnbull used the occasion to declare that "violence against women is one of the great shames of Australia". Ms Cash "reassured" Australians "that all women in Australia and their children should be safe at home, should be safe on the streets and should be safe online". Suvendrini Perera from Researchers Against Pacific Black Sites said there was a glaring omission in the commitment - the treatment of vulnerable asylum seekers that Australia has sent to Nauru.

"Our government has recently condemned violence against women domestically, but if it is truly committed, it should act to the same kinds of violence being perpetrated in Australia's name abroad," Professor Perera said. As well as Ms Batty's Luke Batty Foundation, other signatories to the letter to Mr Turnbull include the Australian Council of Social Service, the Australian Women Against Violence Alliance, the National Council of Single Mothers and their Children and the Australian Muslim Women's Association. Figures provided by the operator of the centres, Transfield Services, show there were 33 allegations of rape or sexual assault between September 2012 and April 2015 on Nauru. This represents an incident about every month, although refugee advocates insist this vastly understates the true extent of the problem.

Of these, Transfield reported that nine were considered major or critical incidents. Over the same period, there were 263 incidents of self-harm in Nauru, or once every four days. In addition, there were 211 reports of assaults judged major or critical incidents. As of August, there were 650 asylum seekers on Nauru, including 93 children. On Manus Island there are 936 male asylum seekers. Former Coalition MP Judy Moylan, ex-WA premier Carmen Lawrence and business woman Janet Holmes a Court are among 20,000 women to have signed a separate petition urging the removal of asylum seekers from the offshore centres.

On Thursday, 445 academics from the University of Sydney wrote to Mr Turnbull demanding he intervene amid "overwhelming evidence" of "repugnant" acts of abuse on Nauru and Manus Island Last week, Liberal MP Russell Broadbent urged Mr Turnbull to fix the "weeping sore" of offshore detention starting with the removal of children. Follow us on Twitter