"Rubbish," Ms Bishop flatly responded to one journalist on Twitter. "Read what I actually said."

To another, she replied: "Also rubbish. Read what I said."

Prime Minister Malcolm Turnbull said on Friday there was no need for Ms Bishop to apologise for the August fracas, in which she said it would be "very difficult" to trust Labour MPs in the event the party formed government – comments newly minted New Zealand Prime Minister Jacinda Ardern described at the time as "highly regrettable".

A Fairfax Media investigation earlier this year led to the revelation Deputy Prime Minister Barnaby Joyce was a dual citizen of Australia and New Zealand – potentially rendering him ineligible to serve in Australia's Parliament.

The High Court is expected to rule on Mr Joyce's case, and that of six other current and former parliamentarians, in coming days.

The case inflamed tensions between the two countries when it was revealed an Australian Labor figure made contact with NZ Labour MP Chris Hipkins about Mr Joyce's case, before questions were raised on the matter in New Zealand's Parliament.

The NZ Minister of Internal Affairs, Peter Dunne, confirmed it was Fairfax Media's investigation that led to the discovery of Mr Joyce's dual citizenship and the subsequent political crisis.

Ms Ardern said Mr Hipkins' conduct was wrong.

"From my perspective, we've made it clear it shouldn't have happened but ultimately it was questions raised by the media that caused this situation, rather than questions from us," she said.

"I wanted to make clear our level of involvement because we've been implicated far beyond what we should have been."

Ms Bishop was scathing about Mr Hipkins' actions, but went further, saying the matter had the capacity to undermine the trans-Tasman alliance.

"New Zealand is facing an election," Ms Bishop said. "Should there be a change of government, I would find it very hard to build trust with those involved in allegations designed to undermine the government of Australia."

Asked to clarify, Ms Bishop doubled down.

"I would find it very difficult to build trust with members of a political party that had been used by the Australian Labor Party to seek to undermine the Australian government," she said.

Prime Minister Malcolm Turnbull went so far as to accuse Labor leader Bill Shorten of wanting "to steal government by entering into a conspiracy with a foreign power".

Ms Ardern later said Ms Bishop's "false claims" were "highly regrettable", and said she had registered her disappointment with the Australian High Commission.

"I greatly value New Zealand's relationship with the Australian government. I will not let false claims stand in the way of that relationship," she said.

"I would happily take a call from Julie Bishop to clarify matters. I have also contacted the Australian high commission to register my disappointment and will be meeting with the high commissioner later today."

Asked if his Foreign Minister should offer an apology to the incoming New Zealand leader, Mr Turnbull said no.

He declared the long-standing relationship between the two countries would not be materially harmed by the incident.

"You're better off not scratching away at past political episodes. I'm looking forward to a great relationship with the new government. [Ms Ardern] is committed to it, I had a very good discussion with her last night," the Prime Minister told Melbourne radio station 3AW.

In an interview with Channel 9 on Thursday night, Ms Bishop described the dispute as in the past.

"The fact is, Ms Ardern gave an explanation a couple of months ago about the behaviour of a New Zealand member of the Labour Party," Ms Bishop said.

"She said at the time that his conduct was wrong, it was unacceptable, it should never have happened, and he should never have become involved. I accepted her explanation and I agree with her absolutely."

Labor's foreign affairs spokeswoman Penny Wong, who was critical of the "most unwise" remarks at the time, said Ms Bishop needed to repair the damage.

"I am actually very surprised thats she is taking the approach she has taken since the [Ardern] government was elected," Senator Wong told Sky News.

"Not only doubling down but really lashing out at people pointing out the obvious, which is that a foreign minister of Australia shouldn't be playing domestic politics with foreign affairs and more importantly, shouldn't be suggesting that...she'd find it hard to work with a Labour government in New Zealand."

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