But Ardern's comments seemingly fell on deaf ears, as Morrison confirmed that Australia would make no changes to its deportation policies.
Australia's policy was "not directed to any one country or any one nationality whatsoever", Morrison said.
"It is a statement of Australia's immigration and border laws that if people that are not citizens commit crimes in Australia, then they have violated the terms of being in this country."
But Ardern said these policies were having a "corrosive" impact on the two countries' relationship.
She was highly critical of the way New Zealanders living in Australia were being treated.
"We appreciate that many Kiwis have taken up the opportunity to live and work in Australia - many more than has happened in reverse," she said.
"Not every Kiwi migrant will be perfect, but evidence shows that the vast majority are providing a net benefit to Australia."
She pointed out that Kiwis in Australia earn more, are more likely to be employed and pay more tax than their Aussie-born counterparts - they are Australia's best migrants.
"But rather than them being given security to keep contributing, in return, their rights have been eroded."
She then moved on to the topic of deportation.
She said Australia is well within its rights to deport individuals who break its laws – New Zealand does the same, she pointed out.
"But we have a simple request. Send back Kiwis, genuine Kiwis - do not deport your people and your problems."
She said Australia had deported more than 2000 individuals and amongst them, there would have been "genuine Kiwis" who do have to learn the consequences of their actions.
But she pointed out that amongst those 2000 were individuals who were too young to become criminals.
"They were too young to become patched gang members. Too young to be organised criminals."
She said the two countries do not want a "race to the bottom" on this issue.
She added that the two leaders remain confident that by continuing to work together, they would find a solution.
"We will own our people. We ask that Australia stop exporting theirs."