Jacinda Ardern has stepped up her criticism of Australia's policy to deport New Zealand criminals as "wrong" and "unjust", saying she will continue to push for change.

Key points: Peter Dutton rejects Jacinda Ardern calls for Australia to stop deporting New Zealanders

Peter Dutton rejects Jacinda Ardern calls for Australia to stop deporting New Zealanders The New Zealand Prime Minsters has repeatedly said it's a "corrosive" policy

The New Zealand Prime Minsters has repeatedly said it's a "corrosive" policy She discussed the policy when she met with Prime Minister Scott Morrison in Melbourne

The New Zealand Prime Minister met with her Australian counterpart, Scott Morrison, in Melbourne on Friday morning, in their first face-to-face talks since the Coalition won the May election.

Top of the agenda for Ms Ardern was the ongoing concern about Australia deporting New Zealanders convicted of criminal offences, some of whom had spent most of their lives in Australia.

"If something's wrong and if something is not fair and is unjust, you don't let it go," she told NZ media after the meeting with Mr Morrison.

"I totally accept that it is within Australia's rights to deport those who engage in criminal activity in Australia. But there are some examples that will not make any sense to any fair-minded person."

Successive New Zealand governments have raised concern with the policy, after more than 1,500 Kiwi criminals were deported since the rules were tightened in 2014.

Ms Ardern repeated her warning that the issue was having a "corrosive" impact on the relationship between the two countries.

"I just think we can't take our friendship for granted, we can't take our closeness for granted. And if there is something that is causing concern for one side of a friendship, it should be raised.

"I just ultimately think New Zealanders look at this policy and just think that's not … fair dinkum."

Speaking ahead of the meeting between Ms Ardern and Mr Morrison, Home Affairs Minister Peter Dutton insisted the policy would not change.

"We need to stand up for Australians," Mr Dutton told Channel Nine.

"And the New Zealand Prime Minister is rightly doing that for her people.

"But where we've got Australian citizens who are falling victim in certain circumstances where people are sexually offending against children, for example, we've had a big push to try to deport those paedophiles."

Mr Morrison met with Ms Ardern today in Melbourne for the first time since the election. ( AAP: Julian Smith )

Ms Ardern and Mr Morrison also discussed global trade and the development of the Pacific, along with ways to combat extremist material being shared on social media in the wake of the Christchurch massacre.

Another policy area where the Australian Government is unlikely to shift is New Zealand's ongoing offer to resettle refugees housed in offshore detention on Manus Island and Nauru.

Canberra has repeatedly knocked back the offer, suggesting it could provide asylum seekers with a "back door" into Australia, given the immigration regime between the two nations.

Ms Ardern said New Zealand's offer to resettle refugees housed in offshore detention was not raised in her discussion with Mr Morrison.

"The offer has been made, it's acknowledged, it's known," she said.

"And I don't think for a moment there's any question that Australia knows that offer still stands."

However, there is a sense among some in the Government the offer may be accepted once the existing resettlement deal with the United States is exhausted.

That agreement, made by Malcolm Turnbull and Barack Obama, angered Donald Trump. But US authorities have accepted some refugees under the arrangement.

PNG wants asylum seeker processing ended

Ms Ardern's trip came ahead of a visit this weekend by Papua New Guinea's Prime Minister, who called on Australia to provide a timeline for ending asylum seeker processing on Manus Island.

"We'd like it to be ended as soon as possible," Prime Minister James Marape told the ABC.

"I've met Immigration Minister Peter Dutton already, I've asked him to expediate the process of phasing out the issue of asylum seekers.

"We need to establish a timeline going forward. The genuine refugees and the non-genuine refugees, what happens to the residual we have in-country?"

Mr Dutton's office revealed the Minister had visited PNG earlier this week and held a meeting with Mr Marape.

"The meeting was positive and productive. We have reduced significantly the number of people Labor put on Manus and now we are pushing to get it as close as we can to zero," Mr Dutton said in a statement.

"Prime Minister Marape and I were in absolute agreement in wanting to get refugees off Manus, and one option we discussed was for people to be settled in Port Moresby, where already almost 60 refugees have settled and [are] making a new life for themselves," he said.