Labour has sunk below National in the latest OneNews/Colmar Brunton poll, 43% to 44%.
The Otago Daily Times said it is the first poll since Simon Bridges took over the National Party leadership in February.
But Labour's partners in Government, New Zealand First and the Green, are both on or above five percent and the three parties combined would translate to 66 seats in the House, comfortably ahead of National and Act with 55 seats.
Labour has sunk by five points, but political commentators said its last poll at 48% seemed unusually high.
The ODT said support for Prime Minister Jacinda Ardern as preferred Prime Minister was down by four points to 37% but she was well ahead of the 10% for Bridges, who replaced former Prime Minister Bill English in February.
Deputy Prime Minister and New Zealand First leader Winston Peters is on 5%, up 1 point.
The party vote result was: Labour 43% - down 5; National 44% - up 1; Greens 6% - up 1; NZ First 5% - up 2; Maori Party 1%- no change.