Labor says it is willing to compromise on a bill that would see children removed from detention on Nauru.
Prime Minister Scott Morrison has been facing immense pressure to get mentally and physically sick refugee children and their families off the Pacific island.
The bill has been sitting in parliament for two years and would see New Zealand resettle asylum seekers and their families.
But part of that deal is that resettled refugees would be banned from ever entering Australia.
It comes only a day after senior Labor MP Tony Burke said there were "deep, deep" problems with the proposal.
Opposition immigration spokesman Shayne Neumann says Labor is willing to work with the government, and sent a letter to Immigration Minister David Coleman on Monday night outlining three amendments.
One of Labor's conditions is for the lifetime ban on entering Australia to only apply to the cohort in Nauru going to New Zealand.
Deputy Labor leader Tanya Plibersek said the lifetime ban proposal was a step too far.
"They do not need this legislation, it's extreme overkill. I think the government is making all sorts of fear claims," Ms Plibersek told reporters in Canberra on Tuesday.
Mr Neumann said the time had come for the government to meet Labor halfway.
"We have listened to the community and the government should do this as well - these kids have languished for far too long," Mr Neumann told ABC TV on Tuesday.
"You can be strong on border protection, resettlement, but the truth of the matter is these people have stayed there too long."
The Greens have also changed their tune, with leader Richard Di Natale saying 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.
Meanwhile, Australian Border Force 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 on Monday, with ABF saying an unknown number of adult refugees and asylum seekers had travelled with them.
Fifty-two children remain on the island.
About 652 people, including 107 families, were on Nauru, while 626 men were on Manus Island in Papua New Guinea, Border Force told Senate estimates.
Home Affairs chief medical officer Parbodh Gogna said medical staff on Nauru have witnessed a huge jump in medical issues.
"They had seen an unprecedented jump in people presenting to the facilities in the last couple of months," he said.
Australian Associated Press
