Support for New Zealand's current flag is still twice that of the alternative.
A telephone poll taken by UMR Research from February 25 to 29 says 59 per cent of New Zealanders want to keep the current flag while 32 per cent want to change. About 9 per cent are unsure.
The poll of 750 voters was released on Friday just as ballot papers for the referendum started arriving in letterboxes.
In the last UMR poll in January, 65 per cent said they would vote for the current flag while 35 per cent would vote for change.
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Prime Minister John Key says it's a once in a generation opportunity.
"If you don't change the flag and that's the majority view, I'll absolutely respect that," he said on Thursday.
"But you won't easily get another chance ... it's a once in a generation chance to choose."
The postal ballot referendum runs from Thursday to March 24, offering voters a choice between the existing flag and the alternative silver fern design.
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The first referendum selected the Kyle Lockwood-designed silver fern flag as the most popular among five alternatives.
Mr Key wants change and wears the silver fern flag on his lapel.
