Prime Minister Jacinda Ardern has vowed not to give up her fight against Aussie lawmakers who don't appear to be giving up any ground in the debate over the fate of some New Zealand deportees.

Although Ardern's meeting with Australian Prime Minister Scott Morrison was not an official bilateral meeting, Ardern put the spotlight on the meeting by saying she intended to bring up an issue which was having a "corrosive effect with our relationship".

She is not happy with the fact some people, who have little connection with New Zealand, are still being deported.

After speaking with Morrison, she called the policy "unjust and unfair".

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The issue was raised with Morrison and Ardern said he had "registered" the concerns.

However, Morrison's Home Affairs Minister Peter Dutton came out a lot stronger earlier in the day.

"Where we have Australian citizens who are falling victim in certain circumstances where people are sexually offending against children for example, we have had a big push to try to deport those paedophiles and people who have committed those crimes," he told the Nine Network.

"I believe strongly that the Australian people would support that stance as well."

Prime Minister Jacinda Ardern was surprised with a gift for daughter, Neve. Photo / Julian Smith
Prime Minister Jacinda Ardern was surprised with a gift for daughter, Neve. Photo / Julian Smith

Ardern clearly disagrees and said New Zealanders would look at the policy and would not think it was "fair dinkum".

She promised to continue to bring the issue up.

"I don't think just because we haven't seen movement, it's an issue we should drop."

She said she would continue to do so, "regardless of whether or not I see any positive moves on Australia's side".

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Despite her setback with Morrison, Ardern said the trip was "absolutely" a success.

Her talks with businesspeople and investors were a highlight, she said.

At a business breakfast on Friday, Ardern talked up the relationship between New Zealand and Australia.

She cited research from the McKenzie Institute, which found there were no two countries closer than Australia and New Zealand.

Aussie PM Scott Morrison meets with NZ PM Jacinda Ardern in Melbourne. Video / Jason Walls

A recent poll from Lowy came to a similar conclusion.

Ardern's message was similar when she met with a group of investors and a New Zealand Trade and Enterprise (NZTE) lunch the day before.

"You are helping New Zealand to thrive," she said.

"Australia has long been a firm part of that [business] ecosystem and will continue to be, but unlike any other."

At both events, she was encouraging investment into New Zealand's small and medium businesses.

Despite the smiles and friendly words, there was a dark shadow hanging over the business end of Ardern's trip.

Aussie fund managers appear to be shocked the Reserve Bank of New Zealand's (RBNZ) stance on increasing banks' capital buffers.

Ardern said she raised the deportations, and that Morrison
Ardern said she raised the deportations, and that Morrison "registered" the concerns. Photo / Supplied

Business people have been raising concerns and questions remain as to if it might damage the two countries commercial relationship.

But concerns about the Reserve Bank and this issue did not come up at the New Zealand Trade and Enterprise (NZTE) lunch, according to Ardern.

The question and answer session of that event was closed to the media.

Ardern said those issues were not raised by Morrison or herself in the meeting.

But when asked if officials brought it up, she dodged the question.

"What matters to me is whether it was raised by PM Morrison and it wasn't."

She said she saw "absolutely no" interest in him in discussing the issue.

Although Ardern might not have come away from the meeting with Morrison with the commitment she might have wanted, she would take some comfort in the fact she was received well by the people of Melbourne.

Nowhere on her trip was this more on display than when she delivered the keynote speech at Australia and New Zealand School of Government (ANZSOG).

Prime Minister Jacinda Ardern has vowed to keep pressing the issue of Kiwi deportations, even if Australia isn't budging. Photo / Julian Smith
Prime Minister Jacinda Ardern has vowed to keep pressing the issue of Kiwi deportations, even if Australia isn't budging. Photo / Julian Smith

The theme of her speech was "why good governance matters" – a topic that wouldn't normally draw much of a crowd but Ardern pulled in more than 2000 people.

Speaking to city officials before Ardern's speech, Melbourne's Lord Mayor Sally Capp said there was a lot of hype about Ardern and the speech.

"The energy started 48 hours ago and it's been brought into a crescendo this afternoon."

Even Ardern was surprised at the level of excitement.

"Thank you for calling a speech called 'good governance matters' a crescendo – very few people would characterise a speech of that nature in that way."