Ball in Australia's court on Nauru refugees, says Jacinda Ardern in post-Cabinet press conference

Prime Minister Jacinda Ardern says that if Australia took up New Zealand's offer to take 150 refugees and asylum seekers from Nauru, she would expect women and children to be prioritised.

But she said the ball was still in Australia's court, in light of the political pressure there to take children from detention centres in Nauru and take up New Zealand's offer.

"We've been consistent. The offer stands. We've made provision to act on the offer. But it is still ultimately a matter for the Australian Government," she said during her post-Cabinet press conference this afternoon.

She said the United Nations High Commissioner for Refugees would screen any refugees coming to New Zealand from Nauru, and she expected UNHCR to prioritise women and children as well - should that eventuate.

"We've always said that we would want to see children in particular, and women and children in particular priority."

The Government is watching political developments in Australia to see if its offer to take 150 refugees and asylum seekers from Nauru might be accepted.

Ardern says the offer remains on the table. Last week three Federal Liberal MPs and close to 6000 doctors pleaded with Australian Prime Minister Scott Morrison to take children off Nauru so they could receive proper medical care.

Australia has long said that it is unwilling to accept the offer because of the "open borders" policy, which makes it relatively easy for Australian and New Zealand citizens to travel and work in both countries.

But Morrison has said that he is open to taking up the offer if a bill passes that would ban people removed from offshore detention centres from travelling to Australia.

Last night Labor ramped up pressure on Morrison, announcing it would support the bill if the Government accepted New Zealand's offer, sent all children and their families in detention centres in Nauru to New Zealand, and only applied the travel ban to those heading to New Zealand.

Morrison responded today by saying he would take advice on the matter, but border protection was not something that could be horse-traded.

Incoming independent MP Kerryn Phelps has also said she wants to prioritise helping the children in detention centres leave Nauru.

Eleven children were transferred off Nauru yesterday for medical attention, leaving 52 minors on the island, according to Australian Border Force officials.

Immigration Minister Iain Lees-Galloway said that nothing had changed from New Zealand's point of view.

"Our offer still stands. As to the matter of who gets to cross Australia's border, that is a matter for Australia."

Foreign Minister Winston Peters has raised concerns that if the bill became law in Australia, it would effectively create two classes of citizens in New Zealand: those that could freely travel to Australia, and those who could not.

He said it was unclear if there would be a solution to the political deadlock in Australia.

"At this point in time, we don't know where this is going. It may never even make it through Parliament in Australia."