Te Pāti Māori polled 2.6%, up from 2.2%.
The Opportunity Party also enjoyed something of a surge, polling 3.3%, up from 2.8% last month and 2.3% in April.
The poll has three left-wing parties on 49%, enough to beat the coalition, which polled 47%.
Labour leader Chris Hipkins polled 21% as preferred prime minister, down 2 points from last month and well down from the 26% he recorded in March.
National leader Christopher Luxon continued to trail Hipkins on 20%, although his performance has been more stable, down just 2 points since his most recent peak of 22% back in March.
The poll showed voters continue to disapprove of the coalition, with 51% of voters saying they disapproved compared to 42% saying they approved.
The poll was taken between June 1-10 and has a margin of error of 3.1%.