Cricket and rugby union are traditional grounds of discontent between Australia and New Zealand.

Things are no different in the weekly phone calls between prime ministers Scott Morrison and Jacinda Ardern where the two will jokingly spar about the performance of their respective sporting teams before getting down to business.

It’s a dynamic the pair also share in public: while both leaders will periodically criticise the actions of the other, they enjoy a warm, friendly and good working relationship. But the historical closeness of the two countries and their leaders is being tested like never before.

Ardern last week sensationally accused Australia of abdicating its responsibilities by cancelling the citizenship of a dual national linked to Islamic State. Melbourne woman Suhayra Aden , who has not lived in New Zealand since she was six, was detained trying to cross the border from Syria to Turkey with her two young children.

It was only the latest incident that demonstrates how strained trans-Tasman relations have become.

Just hours after the New Zealand Prime Minister’s comments, she was on the phone with her Australian counterpart.

While Morrison agreed to keep working on the issue with Ardern, he made no concessions publicly. At a press conference several hours after Ardern’s comments, he insisted Australia would put its “national security interests first”.

While the leader-to-leader relationship remains warm, there is a growing list of areas where the trans-Tasman relationship is straining.

Behind the scenes, tensions between Canberra and Wellington have been building for years, with Ardern repeatedly criticising Australia for deporting Kiwi citizens.

But it is the question of how to handle the growing assertiveness of China that has caused the biggest tensions.

In January, New Zealand’s new Trade Minister Damien O’Connor suggested Australia should speak with more “respect” and “diplomacy” towards China. Shortly after the television interview, Morrison and Ardern spoke on the phone.

It wasn’t a dressing down; the Australian Prime Minister calmly stated his frustrations with the comments and Ardern was receptive to his concerns.

• Facebook 'tentatively' friends Australia again after widely criticised news block
• How China is remaking the world in its vision
• New Zealand Members Of Parliament Discuss Future Of CANZUK
• CANZUK: A new Commonwealth agreement?

A few weeks earlier the country’s Foreign Minister Nanaia Mahuta had offered to mediate a truce between Canberra and Beijing, saying “both parties will have to be willing to come together and concede in some areas where they are currently not seeing eye to eye”. It was a remarkable proposition that a minister just months into the job could solve one of the thornier diplomatic problems in the world.

Morrison, Foreign Minister Marise Payne and senior Australian diplomats could barely hide their frustration at Mahuta’s and O’Connor’s comments. They believe it was harmful to the region’s security and an awful case of “false equivalence” that sent a bad message to regional allies, according to senior figures in the government familiar with the matter.

Australia has been slapped with billions of dollars in trade strikes from Beijing over the past year and the Chinese government has refused to return phone calls from Australian ministers. The last thing Canberra needed was its close ally sending a signal to the region that Australia and New Zealand were not united.

While Morrison let Ardern know of his concerns, O’Connor phoned his counterpart, Dan Tehan, to apologise days after the interview on American business channel CNBC in which he made the remarks.

Senior officials in the Department of Foreign Affairs and Trade were then told there wouldn’t be a repeat of O’Connor and Mahuta’s comments; the rookie ministers had apparently been reined in. In her first major speech as foreign minister last week, Mahuta called Australia “our only formal ally and an indispensable partner across the breadth of our international interests”.

Senior figures in the Morrison government separate Ardern’s public criticisms of Australia over deportations and citizenship revocations from the comments from O’Connor and Mahuta on China.

Ardern’s criticisms have always centred on issues affecting New Zealand, while the interventions from her ministers had nothing to do with her country and were deeply unhelpful to Australia.

There is an appreciation that Ardern has been speaking out in favour of her country’s national interest, and a bit of Australia-bashing in her country always plays well domestically.

Meanwhile, there are senior figures in the Australian government who question whether the deportation of New Zealand nationals who have been living in Australia for years is worth the blowback. Some also believe Morrison should accept Ardern’s offer to resettle refugees presently being held on Manus Island and Nauru to send a strong message that the two countries can work together on people movement issues.

Trans-Tasman relations stretch back to before Australia was a country. While the ANZACs were formed in the First World War, soldiers from Australia and New Zealand have been fighting together since the Boer War. Australia is New Zealand’s largest trading partner overall, when goods and services are taken into account.

But there remains significant unease in Canberra over New Zealand’s positioning on China.

Canberra was put off last month by New Zealand being the only member of the Five Eyes intelligence-sharing arrangement not to be in a joint statement criticising the arrests of pro-democracy figures in Hong Kong. While New Zealand’s participation in the intelligence network is not under imminent threat, senior officials within the Australian government have in recent months jokingly referred to the “Four Eyes” as a putdown to Ardern’s government.

They also see the Kiwis as having a lack of ambition on the world stage. New Zealand is hosting the Asia-Pacific Economic Cooperation forum this year, and the Australian government has been pushing for it to hold some of the meetings in person in October or November, including with world leaders. Canberra is yet to hear back on this.

The friction has been exacerbated by the departure of Winston Peters, the New Zealand First leader who was the deputy prime minister and foreign minister in Ardern’s first term. The maverick MP left the scene after Ardern won government in her own right in October. Peters was arguably the biggest friend of Australia inside the government and was a strong supporter of the Five Eyes intelligence-sharing arrangement.

“It says a lot that Winston held the show together on foreign policy, but he really did to a large extent,” one senior Australian official says.

With Peters gone and Ardern in total command of her government, it is suspected O’Connor and Mahuta were trying to state positions they thought their prime minister held.

Australian officials hope that New Zealand’s reticence to join other allies in criticising China will now subside for a few reasons. Firstly, Ardern will likely feel more comfortable in adopting a strong stance towards China now that she will be sharing it with new US President Joe Biden, rather than the divisive Donald Trump.

Secondly, Ardern seemed restrained while New Zealand was negotiating an upgrade to its existing trade agreement with China, which was finalised last month. New Zealand was always annoyed that Australia’s free trade agreement with Beijing granted more access to the Chinese market than its own.

With the latest deal inked, New Zealand has essentially caught up to Australia. Officials in both governments hope the two countries don’t drift apart.