New Zealand Prime Minister Jacinda Ardern has urged Scott Morrison to rethink Australia's "corrosive" criminal deportation policy, which is causing unintended hardship.

Ms Ardern used a media conference in Sydney alongside her Australian counterpart to deliver a blunt message on the policy, which has seen about 2000 people sent back to New Zealand.

"Australia is well within its rights to deport individuals who break your laws. New Zealand does the same. But we have a simple request – send back Kiwis, genuine Kiwis," she said.

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Ardern slammed the blanket law that sent long-term Aussie residents back to NZ. Photo: Getty

"Do not deport your people and your problems."

She said many of the deportees "on any common sense test" identified as being Australian.

"Just a few weeks ago I met a woman who moved to Australia, not much older than one year old," she said.

"She told me she had no connection to our country, but had three children in Australia.

"She was in a crisis centre, having returned to a country she did not feel was her own."

The NZ leader also pleaded with the Morrison government to provide more rights to New Zealanders working in Australia, such as the ability to work as a public servant or access the national disability insurance scheme.

"Evidence shows that the vast majority are providing a net benefit to Australia. They earn more, they are more likely to be employed, and they pay more tax than their Aussie-born counterparts," she said.

"They are Australia's best migrants.

"But rather than them being given security to keep contributing and return, their rights are being eroded."

Mr Morrison said Australia's deportation policy was clear.

"We deport non-citizens who have committed crimes in Australia against our community," he said.

"This policy is applied not specific to one country, but to any country whose citizens are here."

This comes after AFL gun Dustin Martin's ex-bikie boss father attempted to return to Australia following his own deportation in 2017.

Shane Martin had been in Australia for 30 years but had amassed a number of serious criminal charges including trafficking of ecstasy and being armed with intent. Mr Martin was put on a plane back to New Zealand the day after his arrival.

The two leaders also discussed the coronavirus, greater cooperation on indigenous issues, trade and security.

But one area that was missing from the discussion was the their conflicting stances on climate change.

Australia has been widely condemned for worshipping fossil fuels, while New Zealand lead the way in climate action in the Pacific.

Ms Ardern said she wouldn't bring it up this time around, instead choosing to focus on the deportation issue.

Despite the divide, the leaders were able to agree that the strong and supportive relationship between the nations was a source of great comfort in recent times.

"The last 12 months has, if nothing else, demonstrated just how close New Zealand and Australia are," Ms Ardern said.

"Whether it's the fires in Australia, and the hundreds of personnel that have gone from New Zealand to Australia to support them, or Whakaari White Island, or coronavirus, we've had plenty of examples … where we have been extraordinarily close."

Ms Ardern also met with NSW Premier Gladys Berejiklian and Governor-General David Hurley before she returns to New Zealand on Friday night.