The two nations’ flags are both dark blue with the Union Jack emblem in the top left corner.
The only clear difference is that the Australian version also has six white stars, while New Zealand’s has a constellation of four red stars.
Winston Peters, who is temporarily leading the country while Prime Minister Jacinda Ardern is on maternity leave, raised the issue earlier this week and complained: “We got there first with this design.”
The 73-year-old said: “We designed it and they borrowed it and if we wanted to clear the matter up they should change their flag.”
He added: “It must be patently obvious that all over the world people are confused. I’ve been to places like Turkey and elsewhere where they’ve confused our countries on the basis of those flags. It’s not helpful.”
Opposition leader Simon Bridges ridiculed Mr. Peters’ flag preoccupation, accusing him of populism and labeling him “a poor man’s Donald Trump”.
Bridges said New Zealanders he has spoken to are more concerned about issues such as the economy and healthcare.
He said: “They never raised with me changing the Australian flag. That’s weird by even his (Peters’) standards.”
New Zealand adopted its flag in 1902, while Australia’s was not officially recognized until 1954.
However, the Australian version had been used informally since 1901 and both countries say similar designs were common throughout the late 1800s.
New Zealand held a referendum on changing its flag to a silver fern design in 2016, with the proposal defeated 43% to 57%.