George Brandis, the former Attorney-General and current High Commissioner to Britain, confirmed the plan during a radio interview in Britain on Thursday.
According to the Department of Home Affairs, there are 40 children still in detention on the island, all of who will find new homes in Australia within two months.
FILE - This Sept. 4, 2018, file photo shows the bedroom of a teenage refugee in the Nibok refugee settlement.
The government has come under pressure to accelerate the process from independent Members of Parliament (MPs) who hold the balance of power in parliament and the opposition Australian Labor Party (ALP).
It states that 46 children have been born to asylum seekers sent to Nauru since the processing centre was reopened there in 2012. "I haven't been showboating about it", Morrison said on Thursday. But after more than a year of screening, only 439 have found new homes in the U.S.
According to The Australian, the Australian government set the unofficial timeline as it quietly works to remove children and their families.
Home Affairs Minister Peter Dutton said the refusal by a sizeable number of people on Nauru to resettle in the United States indicated they were not genuine refugees.
But more than 600 remain on Nauru, while refugee support groups say some 600 men are still in transition centres on Manus after the camp there was closed late previous year.
"I think we can say it's remarkably good news that these children will now have access to proper medical care in Australia".
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.
Dutton says people who pose a security risk will not be allowed into the Australian community, even if their child is being treated.
A YouGov Gallaxy national poll taken from October 17 to 22 found that 79 percent of respondents wanted the government to take up New Zealand's offer to take 150 refugees.
Refugee advocates are urging the Government to bring the rest to Australia as soon as possible, following suggestions the Government wants them all off Nauru by December.
"All doctors are really concerned that that level will get to the stage where suicidal ideation will become real, that we will either lose children through suicide or lose children through the Resignation Syndrome, where they become so profoundly depressed that they would rather be dead than continue the mental pain that they have at the moment".
Many are taking legal action to be resettled in Australia and the government is contesting cases. "We are anxious, and the situation is getting worse day by day".
The Government has so far rejected an offer from New Zealand to settle 150 asylum seekers there unless it can pass legislation that would prevent them ever entering Australia.