Wellington – Like squabbling siblings, New Zealand and Australia have close ties but also a rivalry that can sometimes turn ugly.That tension spilled into politics on Tuesday, when Australian Foreign Minister Julie Bishop accused New Zealand's opposition Labour Party of conspiring to undermine her government, a claim New Zealand lawmakers said was "false" and "utter nonsense".The unlikely dispute involved Barnaby Joyce, Australia's deputy prime minister. Joyce said on Monday he'd been advised he was a New Zealand citizen and an Australian court was being asked to determine if he should be kicked out of parliament because Australia's constitution bans lawmakers from being dual citizens.If Joyce was disqualified, Prime Minister Malcolm Turnbull's centre-right government could lose its single-seat majority in the House of Representatives, where parties need a majority to govern.But Joyce told Australia's parliament on Tuesday that New Zealand had just told him verbally that his citizenship had been renounced after he requested as much over the weekend, and he was now awaiting written confirmation. Renunciation won't affect the court decision since the case rests on his eligibility to run in the last election.Bishop said Australia's opposition Labor Party had used their New Zealand counterparts to raise questions about Joyce in the New Zealand parliament.'Highly unethical'"This is highly unethical at least, but more importantly it puts at risk the relationship between the Australian government and the New Zealand government," Bishop told reporters in Canberra."New Zealand is facing an election," she 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."New Zealand's election is next month.New Zealand Labour Party Leader Jacinda Ardern said the claims were false and "highly regrettable". She said she'd contacted the Australian High Commission to register her disappointment and would be meeting with the commissioner in person.Bishop was referring to two questions lodged in the New Zealand parliament by Labour lawmaker Chris Hipkins, who asked whether children born in Australia to a New Zealand father automatically had New Zealand citizenship.Ardern said she had no knowledge of the questions lodged by Hipkins and knew nothing about the Joyce case until it broke in the media this week.'So much utter nonsense'She told Radio New Zealand that somebody connected with the Australian Labor Party had put the questions to Hipkins without mentioning Joyce, and that Hipkins wouldn't have asked them if he knew how they were going to be used. She called the questions inappropriate."I greatly value New Zealand's relationship with the Australian government," she said in a statement. "I will not let false claims stand in the way of that relationship. I would happily take a call from Julie Bishop to clarify matters."New Zealand's Internal Affairs Minister Peter Dunne said Hipkins had not started the row."This is so much utter nonsense – while Hipkins' questions were inappropriate, they were not the instigator," Dunne tweeted. "Australian media inquiries were."Joyce is perhaps best known abroad for the tough stance he took on Johnny Depp's pet dogs Pistol and Boo. Joyce threatened to have the Yorkshire terriers euthanised after saying they were smuggled into Australia in 2014 where Depp was filming the fifth instalment of the "Pirates of the Caribbean" movie series.Depp's then-wife Amber Heard pleaded guilty to falsifying an immigration document to conceal the dogs in a private jet. She avoided jail under a deal that included Heard and Depp appearing in an awkward video warning against others breaking Australia's strict quarantine laws.The Australian and New Zealand opposition parties are kindred centre-left parties, although the Australian party uses the American spelling for its name.