Ms Ardern has continued to push New Zealand's offer to accept 150 refugees and asylum seekers from Australia's offshore detention centres since her first face-to-face meeting with her Australian counterpart in Sydney a week ago.
Whether that meeting will go ahead is now in question, after she revealed she'd had another brief chat with Mr Turnbull in passing on Monday morning (local time) but refused to say when any further talks would happen.
Mr Turnbull opted not to take up the offer, but did not rule out accepting the deal at a later stage.
Papua New Guinea's Minister for Immigration and Border Security Petrus Thomas said on Sunday he expected the remaining men at the Manus Island detention centre to leave the site by Monday so they can access, "food, water, medical care and security". "No matter what label you put on it there is absolute need and there is harm being done", she said.
She said New Zealand has the capacity to help the refugees and should be talking with the PNG government directly to solve "this humanitarian crisis".
But National's foreign affairs spokesman Gerry Brownlee said it was "surprising she's chose to go so hard on the Australians".
Government frontbencher Matt Canavan criticised the genuineness of the offer.
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One of Malcolm Turnbull's Ministers Matt Canavan has described it as a publicity stunt by Jacinda Ardern.
The approximately 420 asylum seekers and refugees choosing to remain at the now-closed Manus Island processing centre have been without food, water or medical supplies for nearly two weeks.
"I think it's clear that we don't see what's happening there as acceptable, that's why the offer's there", she said.
Ms Ardern said it was faster to organise the logistics of any deal with Australia.
A woman protester at the gates of the Australian High Commission in Wellington.
The Australia-based Refugee Action Coalition said officials destroyed property in the camp and attempted to destroy water wells that have sustained the asylum seekers for the past two weeks.
The goal of the protest was to prevent anyone inside from leaving, Peace Action Wellington spokeswoman Emma Cullen said.