Australian Foreign Affairs Minister Julie Bishop has sparked an unprecedented diplomatic brawl with New Zealand's opposition by accusing it of conspiring to bring down the Turnbull government, declaring she will not be able to trust it if it wins power next month.

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.