Prime Minister Scott Morrison is open to accepting New Zealand's offer to resettle 150 refugees from Nauru, with one major condition attached.
That those being held in offshore detention never step foot in Australia.
Under proposed laws being refloated by the government, any refugee settled in a third country would be banned from entering Australia, even under a tourist or business visa.
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.
The ban would prevent refugees who came by boat and settled in New Zealand from ending up in Australia.
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.
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.
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