The latest 1 News / Kantar Public poll put the Green Party up 1 per cent on 10, with ACT down on 7 per cent and Te Pāti Māori on 2 per cent.
That would mean National would get 51 seats in Parliament, ACT nine, Labour 45, 13 for the Greens and two for Te Pāti Māori.
In the preferred Prime Minister stakes, the poll put Jacinda Ardern on 33 per cent, down one, while Christopher Luxon was steady on 25 per cent.
ACT leader David Seymour dropped two points to 3 per cent while Green MP Chloe Swarbrick had 2 per cent of the support and Winston Peters 1 per cent.
The poll is the first since the Budget earlier this month but also coincides with a cost of living crisis.
Last week, the Reserve Bank lifted its official cash rate by 50 basis points (half a percentage point) to 2 per cent, and signalled on current conditions, it could reach close to 4 per cent by the end of the year.
National leader Christopher Luxon has criticised the amount of spending in the Budget and has accused the Government of wasteful spending.
In the last 1 News / Kantar Public poll in March, National overtook Labour, with 39 per cent support compared to Labour's 37 per cent.
Ardern was on 46 per cent and Luxon on 45 per cent for the most preferred Prime Minister.
The latest poll was conducted between May 21 and 25 with a sample size of 1002 eligible voters, with half polled online and half via mobile phone, a margin of error of plus or minus 3.1 per cent and 95 per cent confidence, according to 1 News.
