On Monday, Home Affairs Minister Peter Dutton said there were 50 children left on the island and that his intention was to get that to zero, with 200 children in Australia having already been transferred.
Some have languished on Nauru for as many as five years and doctors and refugee groups have expressed increasing concern about their health and well-being.
Peter Dutton, Australian Minister for Home Affairs, says now is not the right time to be sending refugees to New Zealand.
Today, he claimed criticism of poor living conditions among the would-be asylum seekers was offensive to the people of Nauru.
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.
Dozens of asylum seeker families with children have been transferred in recent weeks, with many coming to Adelaide.
While the government has declared its policy a success after a sharp drop in boat arrivals, human rights activists say hundreds of refugees - including children - have been traumatized by the ordeal. Papua New Guinea has male-only facilities and all the asylum seekers there are adults.
Repeatedly asked whether children would be sent to Nauru in the future, Neumann would only restate Labor's support for offshore processing and third-country resettlement. "But especially to these young men who are (at the Manus Island detention centre) for the most part. they are in utter despair with very similar medical indications".
Legal action would continue to force the evacuation of the remaining children and could be extended to about 90 families on Nauru, some of whom with vulnerable adolescents who were detained as kids, the advocate said.
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Under a deal with former American president Barack Obama, 439 people of a potential 1,250 have so far been resettled from Manus and Nauru to the United States.
"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.
"Even when you bring them to Australia, if you leave families with a sense of uncertainty, it is going to be very hard for the children to recover", he added.
Regardless, none will be allowed to settle in Australia.
The Morrison government is insisting none of the children or their families transferred from Nauru to Australia in recent weeks will be allowed to stay in Australia.
"It's taken court hearings and a groundswell from the community to get the government to act to get these kids off Nauru", Newhouse said.
Has Scott Morrison made a policy blunder by setting this end of year deadline for removing children from Nauru?
She said two close friends moved to Australia a few months ago, and it has been good for them because they can finally go to school, make new friends, and go out at night.
A YouGov Gallaxy national poll taken last month found 79 percent of respondents wanted the government to take up New Zealand's offer to accept 150 children and their families. "We have to get these kids off Nauru now".