Photo: The Canadian Press

Australian Foreign Minister Julie Bishop

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 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.

"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."