A Herald DigiPoll published on Friday shows support for National has dropped to below 50% in the past week.
The poll also shows smaller parties, including New Zealand First, gaining support.
The Labour Party has lost support, but the popularity of leader Phil Goff has increased.
National is on 49.5% support, down from 54.2% last week, while Labour is on 28.7% support down from 29.1%.
Support for the minor parties has risen: Greens are up from 10.1% to 12.6%, New Zealand First has increased from 1.7% support to 3.7% and ACT is up from 0.9% to 1.5%.
The poll of 750 voters was conducted from 3 to 9 November. The margin of error is plus or minus 3.6%.