Among countries of the world, Australia and New Zealand are like siblings, with a shared colonial history and close trade, military and cultural ties. They even have a joint holiday to commemorate the sacrifices both nations made in World War I.

So it was something of a shock on Tuesday when Australia’s foreign minister, Julie Bishop, accused New Zealand’s Labour Party of trying to “undermine the Australian government” by exposing the citizen status of Australia’s deputy prime minister.

Revelations surfaced a day earlier that the deputy prime minister, Barnaby Joyce, was a New Zealander by descent.

Four other Australian politicians have resigned or come under scrutiny in recent weeks because of questions about their citizenship. What started out as a minor political scandal now threatens the government of Prime Minister Malcolm Turnbull. The Australian Constitution does not allow people with dual citizenship to be legislators, and if Mr. Joyce is forced to step down, the government will lose its one-vote majority in Parliament.