Australian Border Force (ABF) have confirmed 11 children in detention on Nauru have been transferred to Australia to receive medical treatment.
The revelation came at a Senate estimates hearing yesterday, as ABF said an unknown number of adult refugees and asylum seekers had travelled with them.
About 52 children remain on the island.
Prime Minister Scott Morrison has been facing immense pressure to get sick refugee children and their families off the Pacific island.
Labor and the Greens now say they are more open to considering a bill in parliament that would see New Zealand resettle asylum seekers and their families from the Pacific island.
But part of that deal is that resettled refugees would be banned from ever entering Australia.
Labor said on Monday that there were "deep, deep" problems with the bill.
But opposition immigration spokesman Shayne Neumann on Tuesday said Labor was willing to work with the government on the bill.
"We're prepared to negotiate in relation to this issue to support amendments - it's time for the government to make those amendments," Mr Neumann told ABC Radio.
Greens leader Richard Di Natale said it was time to "put politics aside" and help the "traumatised children".
"If resettlement after that means resettlement in New Zealand with limited restrictions, just on that group, that's something we will consider," Senator Di Natale told the ABC.