Australian Foreign Minister Marise Payne was silent as her New Zealand counterpart Nanaia Mahuta pledged to continue pushing for fairness in deportations.
The Government has consistently raised concerns about deportees being sent from Australia to New Zealand because in many cases, they have no family or connections to return to.
Standing alongside Australian Prime Minister Scott Morrison in Sydney last year, Prime Minister Jacinda Ardern urged Australia to "not deport your people and your problems" to New Zealand.
Her Australian counterpart Scott Morrison said he had no intention of changing the policy, and insisted it was "not directed to any one country or any one nationality whatsoever".
The issue heated up last month when Australian Home Affairs Minister Peter Dutton described a planeload of deportees to New Zealand as "trash".
Mahuta hit back at the time, saying Dutton's comments "only serve to trash his own reputation".
The Foreign Affairs Minister was less outspoken during her press conference with Payne in Wellington on Thursday, but she didn't back down.
"We've certainly moved on beyond those particular comments and the things that needed to be said were said at the time in relation to the statements made," she said of Dutton's remarks.
"I can say that we continue to raise our concerns around the issue of deportations and the impact that it has on New Zealand and we've reflected time again through the Prime Minister and as recently as our conversation today, the level of that concern."
Ardern has acknowledged that Australia is within its rights.
"It just so happens that we strongly disagree with it," she said last month. "On this issue we've been totally consistent. The Australian leadership is very aware of our view on it and it hasn't changed."
But Ardern said she wasn't giving up.
"I don't think it's a matter of if it's a matter you see as unjust you just give up on it. We will continue to raise it so long as it exists."
And neither is Mahuta.
"We do believe that people who for the most part spend their lives in another country and relate to that country, are by and large self-identifying as to where they belong," she said.
"These are matters that have been raised and will continue to be raised and we'll continue to have discussions about how we might address that."
Payne did not comment on the matter. But she did acknowledge that New Zealand's concerns are heard and acknowledged by Australia.
"Australia takes the concerns that New Zealand raises very seriously," she said, when asked about Australia stripping the citizenship of accused terrorist Suhayra Aden.
"We both now acknowledge that the case now has a number of complexities and we will work through those issues in the spirit of this important and deep bilateral relationship - closest of bilateral relationships - particularly in relation to matters concerning children.
"That is something which we have undertaken to discuss from our consultations today."
