Labour and the Green Party have received a small boost in a One News Colmar Brunton poll taken over the period in which the parties announced an agreement to work together.
National is still riding high on 48 per cent - but did not receive any increase in support following last month's Budget.
The poll has put National on 48 per cent (down 2 per cent), Labour on 29 per cent (up 1 per cent), the Greens on 12 per cent (up 2 per cent) and New Zealand First unchanged on 9 per cent.
The poll of just over 1500 eligible voters was taken between May 28 and June 2 and has a margin of error of plus or minus 2.5 per cent.
Labour leader Andrew Little and Green co-leaders James Shaw and Metiria Turei announced on May 31 that they had signed a Memorandum of Understanding.
The agreement includes clauses to work together in Parliament, as well as possibly on joint policies in some areas and a joint campaign.
Colmar Brunton said that following the MoU announcement, support for Labour rose significantly from 26 to 31 per cent, with support for NZ First dropping from 11 to 7 per cent. No other changes were statistically significant, Colmar Brunton said.
On the preferred prime minister question, John Key was steady on 39 per cent, Andrew Little had no change at 7 per cent, and Winston Peters was up 2 percentage points to 12 per cent.
If the poll results were translated to seats in Parliament, NZ First would hold the balance of power.
National (58 seats) and its support parties United Future (1), Act (1) and the Maori Party (1) would fall just short of the 62 seats needed with 122 MPs.
NZ First would have 11 seats, Labour 35 and the Greens 15.