The Coalition is also threatening to take the unprecedented step of using its numbers to refer lower house Labor MPs to the High Court to have their eligibility assessed - completely contradicting the government's position as recently as last week that such referrals should never be partisan.

Mr Joyce referred himself to the High Court on Monday after confirming he was a dual citizen of New Zealand, potentially ruling him constitutionally ineligible to stay on in Federal Parliament.

Labor is demanding he step down from cabinet and abstain from votes in the House of Representatives until the court rules on his status.

But Mr Turnbull is seeking to turn the tables on the opposition, seizing on claims that someone from Australian Labor had a NZ Labour MP ask an official question on notice about the citizenship situation.

NZ Labour leader Jacinda Ardern confirmed her frontbencher Chris Hipkins was involved.

"Yes, someone from the ALP put some legal question to him around citizenship. No mention was made of anyone's name, no rationale for any particular case being pursued was ever raised," Ms Ardern said.

"He asked the questions without knowing how that might be used and has made it very clear, in hindsight, had he known how it would be used, he would not have asked the questions."

Mr Turnbull told the Coalition party room Ms Ardern's comments were a "very serious development", showing that Opposition Leader Bill Shorten was "willing to interfere in the political system of a foreign country".

"The Australian people elected the government. Bill Shorten wants to steal government by entering into a conspiracy with a foreign power," Mr Turnbull said.

However, NZ's Minister of Internal Affairs Peter Dunne said the rhetoric around NZ Labour was completely overblow.

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

Mr Hipkins said he was not directed to ask a question, saying only it arose from a conversation he had with an Australian Labor friend.

Mr Shorten told the caucus on Tuesday the government was "engaging in conspiracy theories" but did not explicitly refer to citizenship doubts over Labor MPs or the accusation of collusion with NZ Labour.

Government ministers are also publicly ramping up pressure on the opposition, with junior minister Michael Sukkar accusing Labor of "borderline corruption" and others signalling several Labor MPs are now in the firing line.

Leader of the House Christopher Pyne has named Labor MPs Justine Keay, Susan Lamb Maria Vamvakinou and Tony Zappia as being under a cloud.

"If they are in the clear, they should produce the evidence. If they haven't got the evidence, they need to have their status clarified by the HIgh Court," Mr Pyne told ABC Radio on Tuesday morning.

"The Labor Party needs to produce the evidence or the government will consider its options."

Manager of opposition business Tony Burke said those politicians caught up by section 44 of the constitution so far - the Nationals' Mr Joyce, the LNP's Matt Canavan, the Greens' Scott Ludlam and Larissa Waters and One Nation's Malcolm Roberts - "would easily be caught by our process".

"What we do is before anyone's allowed to nominate [is] we have to find the country of birth of their parents and of their grandparents and whether their parents or grandparents to their knowledge had any foreign citizenship," Mr Burke told ABC Radio.

"If the answer is yes to any of those, then a team of lawyers will work with the candidate to make sure that all of the requirements of section 44 have been met. So it's a cumbersome process but no one is allowed to have their nomination even put in."

Labor is resisting demands it produce proof that none of its MPs have dual citizenship, claiming its candidate vetting processes prevent any dual citizens from slipping through the cracks.

Asked on Tuesday if Labor had requested that a New Zealand MP ask questions, Mr Burke said "absolutely not to my knowledge".

Mr Joyce told reporters on Tuesday morning he was "shell shocked" by the news.

"I only had it confirmed on Thursday that ... apparently by reason of my father being a New Zealander, I was a New Zealander and now I'm doing everything I can to fix it up and I'm sure the High Court, who are vastly wiser than me, will come up with all the answers."

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