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.