New Foreign Minister Winston Peters says the transtasman relationship has been allowed to deteriorate - saying, "our relationship is not what it should be".
Peters expects to talk to his counterpart Julie Bishop at some stage today, and told media that New Zealand needed to play its part in mending the relationship.
"There are a lot of areas which I don't want to outline now that we have to work seriously on to better our relationship with Australia. I think we can't deny it that here we are in October 2017 and our relationship is not what it should be. I think the Prime Minister, the Labour Party, everyone in this coalition understands that."
In the Newshub leaders debate during the campaign, Jacinda Ardern and Bill English were asked about the Australian Government eroding the rights of New Zealand expats living in Australia, and whether they would retaliate with similar measures.
Ardern said if Kiwis in Australia were locked out of tertiary education, she would lock Australians out here. That would happen only if fees went up significantly for New Zealanders living in Australia.
Peters on the other-hand has long called for New Zealand to officially apologise to Australia for allowing "backdoor" immigration to Australia.
Asked today about Ardern's comments on possible retaliation against Australia, Peters indicated such measures wouldn't be necessary or productive.
"There is a way we can work our way through this and that will certainly be the ambition of New Zealand First and myself. In the end...the greater education of the Australians in New Zealand could only enhance both countries...but on the other side, we need to better understand what volume [of Kiwi students] Australia was taking. And it is not a small amount of money they are talking about."
Another issue that has strained the NZ-Australian relationship is the deportation of New Zealanders living in Australia who have had their Australian visas cancelled after being jailed for 12 cumulative months or more, or failing a character test.
Many of those deportees have lived in Australia since childhood. They are held at detention centres while appealing their deportation.
• Iraq deployment
Labour, NZ First and the Green Party all opposed the joint NZ-Australia training mission at Camp Taji to train Iraqi soldiers.
Asked if New Zealand troops could be brought home earlier than their mandate - November 2018 - Peters said that would be a decision for Cabinet and the Prime Minister.
"I don't think we have a big difference of opinion in this Cabinet on that question. But I would wait to see what the discussion brought forwards."
• Free trade deal with Britain
Peters also indicated a post-Brexit trade deal with Britain will proceed quickly, saying British Foreign Secretary Boris Johnson had already contacted his office to set up a time to talk.
"We are on the same side now," Peters said.
• Defence spending
NZ First's coalition agreement with Labour includes an agreement to "re-examine the Defence procurement programme within the context of the 2016 Defence Capability Plan budget".
New Defence Minister Ron Mark said today that his party had been concerned about the type of expenditure and agreements entered into under the previous Government.
"We will run a ruler over that, stay within the allocation that exists, but seek to get better quality decisions...I really want to see where they are up to."