"We've got cases where someone's been in Australia since they were 6 months old, had no connection to New Zealand at all. It's those cases I consider indefensible.
"There have been examples where they've never set foot in New Zealand, haven't even visited the place."
She said by and large, New Zealanders in Australia punched above their weight in terms of their contribution to the tax system and to the country.
"But we have a few cases, and this is
why I say it's corrosive, there's these little examples where I think probably fair-minded Australians and New Zealanders will just say 'that doesn't seem right'."
Morrison did not give any hint last week that Australia would be changing its laws as a
result of Ardern's concerns.
Foreign Minister Winston Peters went even further today, calling the policy a "festering sore" in the context of justice and humanity.
"When you expel someone from Australia, and the person has never lived in New Zealand but perchance they live in a realm country with special century-old relationship, namely with Cook Islands, is now judged to be a New Zealander, you're at the extreme end of credibility," Peters said in an interview with Sky News Australia.
"All we're saying to our Australian friends is, you have a very similar jurisprudential background as the New Zealand people do. That's not fair and we want you to acknowledge it."
Peters was referring to the case of Wichman Uriaere who has been ordered to be deported from Australia despite having never been to New Zealand.
Uriaere has a New Zealand passport because he was born in the Cook Islands, and is one of more than 1600 New Zealanders ordered to be deported since the beginning of 2015, many of whom have little connection to New Zealand.
Peters cited the case following a meeting with Australia Foreign Minister Marise Payne on Waiheke Island earlier this month.