Australia's deportation of criminals back to New Zealand is being raised in a meeting between Kiwi Prime Minister Jacinda Ardern and Prime Minister Scott Morrison in Melbourne.
She has also promised to talk about child poverty and climate change, which is increasingly affecting smaller Pacific nations.
The two leaders are meeting on Friday for the first time since the aftermath of Christchurch's massacre, in which an Australian far-right terrorist killed 51 people at mosques in March.
Mr Morrison gave Ms Ardern a soft toy rabbit and a book about Australian animals for her daughter Neve, before their meeting at the Commonwealth offices in Melbourne.
The Australian leader acknowledged the strength of the two nations' relationship, noting "we've got a number of issues we're just moving along and keeping in contact with".
"Thank you prime minister for the warmth of your welcome," Ms Ardern said at the start of a round table meeting with Mr Morrison and a team of advisors.
She again congratulated Mr Morrison on his election victory and acknowledged the pair's close contact.
"In the wake of Christchurch, the statement at the G20, the discussions about deployments - I really value the fact that neither of us hesitates to pick up the phone so I just want to acknowledge that," Ms Ardern said.
There was laughter and banter for the cameras and reference to Australia's support for NZ in the final of the recent Cricket World Cup.
"I'm not sure if NZ would have done the same if the role had been reversed," she quipped.
"Our second-biggest trading partner, our biggest source of investment, but also our friends, so it's great to be here with you - thanks for your hospitality."
One issue on which there might be divide is that of Australia's policy to deport criminals to NZ, even if they moved to Australia as toddlers and grew up Australian.
Ms Ardern has said the policy is having a "corrosive" impact on the relationship between the two countries.
Home Affairs Minister Peter Dutton says New Zealand is the only country where a citizen could get a visa to stay in Australia on arrival.
"But we have been very clear, if you come as a New Zealand citizen, a Brit, wherever you come from, your country of origin is where you go back to if you have committed a crime," Mr Dutton told Nine's Today Show.
"Where people are sexually offending against children for example, we have had a big push to try and deport those paedophiles."
Labor leader Anthony Albanese has no plans to change the policy either.
"We think that the balance is essentially right but it's legitimate if there are issues for Jacinda Ardern to raise those with Scott Morrison. We don't want to see this to be a partisan debate," he told Today.
Australian Associated Press