Immigration department figures obtained by Fairfax Media show that there were 33 cases of alleged sexual assault involving children in Australian detention centres and Christmas Island between January 2013 and March 2014. The figures do not extend to Nauru or Manus.

The figures follow allegations of sexual abuse of women and children on Nauru, including underage asylum seekers being forced to perform sexual acts in front of guards; female asylum seekers being told to strip naked in front of guards if they wanted a shower longer than two minutes; and one woman being told she would be raped if she was resettled in the Nauruan community.

On Tuesday, Immigration Minister Scott Morrison broke his silence on the Nauru allegations, saying they were of a "generalised nature" and that he had referred them to his department.

"[The allegations] do not provide details of the identities of the alleged victims or perpetrators or the dates and times of when events allegedly took place," Mr Morrison said.

"The government has put in place additional support to assist the Nauruan government to respond to any incidents and to ensure the welfare of those residing at the centre is properly cared for."

A worker at the Nauru detention centre, who asked not to be named, told Fairfax Media on Tuesday that she often saw children sitting on guards' laps late at night.

"I was told by an Australian guard who was friends with the locals that there was an imminent danger when the asylum seekers were released in regards to violence and sexual abuse," she said.

"As staff, we were always warned about going out into the community alone, especially women, as there had been a few attempted sexual assaults towards staff."

Labor immigration spokesman Richard Marles and former Labor immigration minister Chris Bowen called for the Abbott government to conduct an independent investigation into the allegations.

"These reports are concerning – what we need now is for the government to conduct a proper investigation into the allegations and for this to be done transparently," Mr Marles said.

On Wednesday, Greens senator and immigration spokeswoman Sarah Hanson-Young will move a motion to request all incident reports logged at the Nauru detention centre relating to the misconduct of centre staff and all complaints of sexual assault and child abuse made to case workers in the past 12 months. The senator has also written to Mr Morrison twice, urging him to start an investigation.

"Children resorting to extreme self-harm and further accusations of serious sexual abuse must be addressed by the minister immediately," Senator Hanson-Young said.

"Australian and Nauruan guards, paid for by the Abbott government, have had serious allegations levelled against them. It's time the government acted."

Mr Morrison responded to Fairfax Media, saying: "The government takes these matters seriously. However, we note that the allegations by Senator Hanson-Young have been made publicly and in the context of broader political statements to discredit the government's involvement in offshore processing."

The chief executive of a leading child protection organisation said the allegations of sexual abuse on Nauru needed to be addressed urgently by the Abbott government.

"The government needs to send a specialist police team over there and investigate this immediately because they employed the company," Bravehearts CEO Hetty Johnston said. "The government has a duty of care for these children and they are potentially liable. If they are aware that employees are allegedly harming children, they need to address this. "

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