New Zealand's government has made a dramatic U-turn on its competition to design a new national flag, and is allowing a fifth wild card entry.

Red Flag, designed by Wellington resident Aaron Dustin, experienced a groundswell of public support earlier this month after failing to make the final four for the competition.

PM John Key had previously ruled out making changing the final line-up but nearly 52,000 people have signed a petition calling for it to be added.

But he has now said it will be included in November's referendum, which will ask New Zealanders which of the designs they prefer.

A second vote in 2016 will ask whether they want to scrap the existing flag - featuring the Union Jack - and replace it with the winner.

The four finalists were not well received when they were unveiled earlier this month, with many dismissing them as boring, predictable or too corporate. Three featured a fern design and the fourth the curving koru Maori symbol.

Despite the subsequent massive support, for Red Peak, Mr Key had ruled out including it as a fifth entry, saying doing so would require a change to the law.

But on Wednesday, Mr Key said his party would back a bill tabled by the Green party to amend the New Zealand Flag Referendums Act and allow a public say on Red Peak.

"In the end, I'm not wanting to be the one that stands in the way of people having some choice," he told reporters.

Green Party co-leader James Shaw said it was "kind of ridiculous that it has got to this point", and that Mr Key could have included Red Peak all along if he had wanted to.

The move was both celebrated and mocked on social media.