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Former attorney-general George Brandis has confirmed all asylum-seeker children on Nauru will be relocated to Australia by the end of the year.
But Home Affairs Minister Peter Dutton says he will not allow people who pose a risk to Australia to be allowed out.
"I've had cases before where I've made decisions that the father will stay in custody and the child and the mother will go out into the community," Mr Dutton told 2GB radio on Thursday.
The federal government has set an unofficial timeline to have asylum-seeker children moved from Nauru to Australia by the end of 2018, The Australian reported on Thursday.
"There are hardly any children on Nauru and in New Guinea and we expect that by the end of this year there will be none," Mr Brandis told LBC radio.
It is understood there are 38 children of asylum seekers remaining on the island.
Of the children removed from the Pacific nation during the past few days, 13 have been hospitalised in capital cities across Australia.
Mr Dutton said the government had emptied the Manus Island detention centre and moved all children out of detention.
"We've done it there and we're in the process of doing it in Nauru but we're doing it in a way that's not going to restart boats," he said.
Former Human Rights Commission president Gillian Triggs says it will take time for the children and their families to be healthy.
"These children are, on all the medical evidence, deeply traumatised and damaged," Ms Triggs told ABC radio on Thursday.
Ms Triggs infuriated the government when she investigated conditions for children in immigration detention in 2014, publishing a 300-page report saying they should not be detained.
A total of 46 infants have been born to asylum seekers since Nauru was reopened for processing in 2012.
In recent years, 244 minors have reportedly been taken to Australia from offshore detention centres.
Prime Minister Scott Morrison confirmed the government has been "quietly" removing children from the island nation.
"Children have been transferred off Nauru. That's been happening for some time," he told 2GB.
"I haven't been showboating about it."