New Zealand's acting prime minister has added fuel to a trans-Tasman war of words by claiming Australia copied their flag and should get a new one.

During New Zealand's failed 2016 referendum into replacing its flag, confusion between the Australian and NZ ensigns was often raised by those looking for a change.

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Asked about the matter this week, New Zealand's acting PM Winston Peters - whose party fiercely opposed a change - blamed Australia.

"We had a flag that we've had for a long time, copied by Australia, and they should actually change their flag and honour the fact that we got there first with this design," he told TVNZ.

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Technically, New Zealand adopted its Southern Cross-starred flag in 1902, while Australia formally only did so in 1954.

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However, the Aussie national banner won a competition in 1901 and was flown in September that year during the first Flag Day. It underwent minor changes during the decade.

The comments come amid escalating trans-Tasman tension over Australian deportation of hundreds of New Zealanders.

It the past two weeks Mr Peters, Home Affairs Minister Peter Dutton and New Zealand's justice minister have traded barbs over the matter.