Australian Border Force officials have revealed 11 children were transferred off Nauru today for medical attention, with another 52 minors remaining on the Pacific island.
Officials have amended the figure to 11 after initially saying it was 16.
The update comes as the federal Greens float a compromise agreement that could allow families to resettle in New Zealand with their families.
The Federal Government has indicated it may accept New Zealand's offer to take up to 150 refugees, but only if legislation passes Parliament ensuring people sent to offshore detention can never travel to Australia.
Home Affairs secretary Michael Pezzullo said that legislation, which has been sitting in Federal Parliament since 2016, would close a "back door" to dissuade further boat arrivals.
According to the latest figures, there are 652 people on Nauru, with 541 classed as refugees and 23 as failed asylum seekers. The status of another 88 is yet to be determined.
The United States has accepted 276 people as part of a resettlement deal and rejected an additional 148.
There is growing pressure from crossbench MPs for the government to accept New Zealand's offer, with incoming independent Kerryn Phelps describing the issue as a first priority.
The Greens are now open to considering a travel ban for the group, but only if all children are first brought to Australia for medical treatment, and restrictions only applied to the cohort sent to New Zealand.
"We need to put the politics aside and look after these children, who are being traumatised and brutalised right now," leader Richard Di Natale told the ABC.
"If resettlement after that means resettlement in New Zealand with limited restrictions, just on that group, that's something we will consider.
"What we won't consider is putting bans or restrictions [on] those people who have been left behind."
Greens open to discussions about travel restrictions
The Greens have consistently called for refugees on Nauru and Manus Island to be brought to Australia permanently.
The party's Lower House MP Adam Bandt last week introduced a private members' bill requiring every child and their family be brought from Nauru to Australia for medical assessment.
But the deteriorating mental and physical health of young people on the Pacific island has forced the party to change its position.
The Greens have not explicitly supported the government's current legislation but are open to discussions about travel restrictions if that is what it takes to resettle families.
If the Coalition and the Greens can reach a compromise then legislation could pass through the Parliament.
The Coalition's bill as currently drafted would apply to everyone who arrived by boat since July 2013, including people sent in the United States and Cambodia.
Labor has also strongly opposed the lifetime ban legislation, saying it was over-the-top and unnecessary, but said it would consider the bill "if that's what it comes down to".
"Labor will consider anything because the best interests of these children is what has to be the paramount consideration," shadow attorney-general Mark Dreyfus said.
"The government should not hold them to ransom and insisting on legislation when it's apparent New Zealand isn't insisting on the legislation."