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But if a new flag was chosen in a public referendum, the silver fern was by far the most popular design, the poll showed.
Asked if they felt the time had come for New Zealand to design a new flag for itself, 52.6 per cent of those surveyed said "No" and 40.6 per cent said "Yes".
Prime Minister John Key last week outlined plans for a referendum on a new national flag during the next parliamentary term. Voters would choose whether to keep the current flag or choose from a handful of new designs. Labour and the Greens are supporting the referendum.
The survey found that women, Aucklanders, and older people were more likely to support the status quo, which has been the national flag for more than a century.
The Returned Services Association has been the most outspoken opponent of a new flag, saying soldiers died fighting under the Union Jack and Southern Cross.
But the survey showed that younger people also questioned whether the time was right for the country to move on from its British roots - more than 50 per cent of 18 to 39-year-olds voted against a change.
Public opposition to a new national flag has grown significantly in the past four years. When the same question was asked in 2010, during a Herald campaign for a new flag, 52 per cent of respondents felt the time was right for a change and 44 per cent did not.
A group of eminent New Zealanders will be asked to create a shortlist of new flag designs before the 2017 election, with public input.
Mr Key said he hoped that the process would find a design as distinctive and unifying as Britain's Union Jack or Canada's maple leaf.
"If we choose well, it will become internationally recognisable in a way that our current flag is not, despite more than a hundred years of use."
His preference was for the silver fern on a black background. The symbol was worn by national sports teams and was also carved into the gravestones of New Zealand soldiers killed in battle.
The silver fern was also the most popular choice of all age-groups surveyed in the poll, with 42.9 per cent saying it was the national symbol which they most wanted to have incorporated into a new flag.
The Southern Cross was the second most popular option, closely followed by the koru, which was popular with the younger generation. The Southern Cross was preferred by people over 65.
The poll of 750 eligible voters was taken between March 6 and 16. It has a margin of error of plus or minus 3.5 per cent.