She is expected to pursue the matter further during a meeting at the East Asia Summit in the Philippines this week.
"We haven't scheduled anything, but absolutely it is my intent to talk with him before this meeting concludes".
Ardern said New Zealand "treated citizens as citizens and residents as residents", so was not prepared to give the refugees a different status, but how Australia viewed refugees that might come to New Zealand was a matter for that country.
Ms Adern on the weekend blasted Australia's handling of the issue as unacceptable as she continues to to push New Zealand's offer to accept 150 refugees and asylum seekers from Australia's offshore detention centres.
That has been mooted as a compromise to allay Australian concerns that New Zealand would be seen as a back door to Australia, potentially encouraging more refugees to head for Australia.
The situation inside the detention centre is a "humanitarian emergency", the UN's refugee agency has said, for which Australia holds responsibility. "But there are those now that we are talking about who are actually screened to be refugees".
Asked about criticism of her approach from National foreign affairs spokesman Gerry Brownlee, Ardern said she was happy with how it had been handled.
Approximately 420 asylum seekers are refusing to leave the Papua New Guinea detention centre over fears for their safety from locals. Ms Ardern said she would not change New Zealand law to prevent this from happening. I stand by the way that we've managed the situation.
"If they did, that would be their decision".
"Perhaps it is these every day physical reminders that explain why New Zealanders to this day place a high premium on peace".
Responding to reports PNG authorities were preparing to remove refugees and asylum seekers from the now-closed facility on Thursday, Jacinda Ardern said she wanted to raise the issue with Mr Turnbull at APEC.
"That would not be our intent to do that - we treat citizens as citizens and residents as residents".
There have been calls for Ms Ardern to deal with Papua New Guinea officials directly.
Four hundred and twenty-one refugees and asylum seekers holed up in the Manus Island detention centre have been told by Papua New Guinea's government they must leave on Monday or face forcible eviction, as another legal challenge goes to court, and global pressure continues to mount on Australia to intervene. Australia's prime minister, Malcolm Turnbull, most recently refused it earlier this month.
"I don't think anyone should underestimate the size of the issue Australia is facing here".
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