Prime Minister Scott Morrison is willing to accept New Zealand's offer to resettle 80 asylum seeker children and their families from an offshore detention centre on Nauru.
But there's one condition - that they never step foot in Australia.
Under proposed laws being refloated by the federal government, any refugee settled in a third country would be banned from ever entering Australia, even under a tourist or business visa.
The Labor opposition says the bill is an unworkable overreach, given immigration minister can already use their powers to stop individuals entering the country.
The bill has been stuck in parliament since November 2016.
"That's the government's bill and it's not supported by the crossbenchers, it's not supported by the Labor Party, or the Greens," Mr Morrison told reporters in Canberra on Wednesday.
Independent senators have now asked for an urgent briefing on the bill.
"I'm wondering what's taken two years to request one," Mr Morrison said.
Mr Morrison is talking down the prospects of putting the bill to the vote this week.
"There is no support for that bill at present," he said.
New Zealand has long held the view that any such arrival bans are a matter for Australia.
"Our offer still stands. Who Australia allows across their borders is a matter for the Australian government," New Zealand Immigration Minister Iain Lees- Galloway told AAP.
The development comes as Labor drafts legislation in response to growing concerns by Australian doctors about the care provided to children and their families on Nauru.
They want to speed up medical transfers of sick children to Australia.
Three Liberal MPs have also taken the extraordinary step of demanding the prime minister get children off the Pacific island, citing serious fears about their health.
Nationals frontbencher Darren Chester says he is sympathetic to the concerns of his coalition colleagues, but would be "deeply troubled" by any softening of Australia's border protection rules.
