Ms Bishop's was quickly accused of risking Australia's relationship with one of its closest allies after the extraordinary intervention in New Zealand's impending election, which earned a sharp rebuke from the NZ Labour leader Jacinda Ardern.

A Fairfax Media investigation into Deputy Prime Minister Barnaby Joyce confirmed on Monday he was a dual New Zealand national, which could disqualify him from Parliament. Mr Joyce referred himself to the High Court, plunging the government into fresh crisis.

But the government sought to turn the tables on Labor on Tuesday, seizing on claims an ALP staffer had recently made contact with an New Zealand Labour MP about the issue.

Ms Bishop led the attack, but her conspiracy charge was strongly backed up by Prime Minister Malcolm Turnbull, who accused Opposition Leader Bill Shorten of trying to "steal government by entering into a conspiracy with a foreign power".

Fairfax Media can reveal it was Labor frontbencher Penny Wong's chief of staff, Marcus Ganley, who contacted New Zealand MP Chris Hipkins. It's understood Mr Ganley, who is from New Zealand, spoke to Mr Hipkins about citizenship laws but did not mention Mr Joyce.

Mr Hipkins subsequently asked a number of questions about Australia-New Zealand citizenship laws in the New Zealand Parliament.

Ms Bishop warned the "collusion" between the two parties could damage relations between the two countries, describing the involvement of Senator Wong's office as "utterly disgraceful" and "tawdry".

"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.

"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."

Ms Ardern hit back at Ms Bishop, saying her "false claims" were "highly regrettable".

"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."

Ms Ardern later met with Australia's High Commissioner to New Zealand, Peter Woolcott, to register her disappointment.

Senator Wong confirmed the intervention after her office was contacted by Fairfax Media on Tuesday.

"A staff member in my office had informal discussions with New Zealand friends about domestic political issues, including the section 44 debate," Senator Wong confirmed.

She said she and her staff had no knowledge that any questions had even been asked until after the story broke on Monday.

"New Zealand Minister Peter Dunne has since confirmed it was questions by Fairfax journalists, and not the question on notice, which led to the outing of Mr Joyce as a New Zealand citizen," Senator Wong said.

"For the Turnbull government to then turn this into a diplomatic incident to try to distract attention from the failings of the Deputy Prime Minister is both reckless and damaging."

Labor dismissed the government's attack as an attempt to distract from Mr Joyce's eligibility to remain in Parliament.

New Zealand Interior Affairs Minister Peter Dunne - who is a member of the ruling conservative government, not Labour - also slammed the conspiracy claims.

"This is so much utter nonsense - while Hipkins' questions were inappropriate, they were not the instigator. Australian media inquiries were," he said, referring to questions from Fairfax Media.

Mr Hipkins says he was not directed to ask the questions but rather did so out of curiosity. Ms Ardern said she had counselled her MP that it had been inappropriate to ask the questions.