The Turnbull government has become embroiled in a trans-Tasman diplomatic spat after accusing Labor and its New Zealand colleagues of a “conspiracy” over the Barnaby Joyce citizenship affair.

Prime Minister Malcolm Turnbull said on Tuesday that Labor had “conspired” with NZ Labour to “undermine” the sovereignty of the nation, while Foreign Minister Julie Bishop went further by suggesting she would find it hard to work with a newly elected NZ Labour government.

It followed revelations a Labor staffer had asked a NZ Labour politician to enquire about the country’s citizenship laws in Parliament.

“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,” she said.

The diplomatic spat comes with NZ in the throes of an election campaign.

Opposition Leader Jacinda Ardern hit back on Tuesday, saying Ms Bishop’s “false claims” were “highly regrettable”.

NZ Labour’s Jacinda Ardern hit back at Ms Bishop on Tuesday. Photo: AAP

“I would happily take a call from Julie Bishop to clarify matters,” she said.

Following a meeting with the Australian High Commissioner, Ms Ardern said she would call Ms Bishop herself but did not have her phone number.

Ms Bishop’s accusations came despite NZ’s Internal Affairs Minister Peter Dunne dismissing suggestions that two parliamentary questions from a NZ Labour MP had prompted the NZ government to investigate Mr Joyce’s situation.

“This is so much utter nonsense − while [NZ Labour MP Chris] Hipkins’ questions were inappropriate, they were not the instigator. Australian media inquiries were,” Mr Dunne tweeted.

NZ’s Foreign Minister Gerry Brownlee described NZ Labour’s conduct as “inexplicable” while Prime Minister Bill English accused the party of interfering in Australian politics.

Labor’s foreign affairs spokeswoman Penny Wong labelled Ms Bishop’s comments “extraordinary” and suggested that the government was trying to “distract attention” from Mr Joyce’s failure to renounce his New Zealand citizenship.

Labor poured scorn on the Deputy PM’s decision to remain in his job during question time as it sought to force his resignation.

Government MPs faced questions about Barnaby Joyce. Photo: AAP

Referring to Ms Bishop’s comments on Tuesday, Labor’s Tony Burke asked the PM: “[If] the Foreign Minister won’t be able to work with the New Zealanders, how will the Foreign Minister be able to work with the Deputy Prime Minister?” 

Mr Joyce confirmed NZ authorities had informed him his citizenship had been renounced, paving the way for him to run in a by-election if his election was struck out by the courts.

Parliamentarians were scrambling to confirm their citizenship on Tuesday, with the government hinting that it may refer four Labor MPs to the High Court.

The government claims those MPs – Tony Zappia, Justine Keay, Maria Vamvakinou, Susan Lamb – have questions to answer, while Labor has raised raised doubts about Liberals Julia Banks and Ann Sudmalis.

The Nationals leader and Ms Bishop accused Labor of “treachery” during the Coalition’s joint party room meeting on Tuesday morning.

The Deputy PM’s predicament also provoked a response from his old foe, actress Amber Heard, who had fought with Mr Joyce over Pistol and Boo, the dogs she had once brought into Australia with ex-partner Johnny Depp.

“When @Barnaby_Joyce said “no one is above the law” I didn’t realise he meant New Zealand law,” she wrote on Twitter.

https://twitter.com/realamberheard/status/897254836697157632

Amid the controversy, independent MP Bob Katter on Tuesday withdrew his guarantee to support the government in the lower house.

Mr Katter is one of the crossbench MPs that pledged to ensure the Turnbull government runs its full term.