The poll gap between National and Labour narrowed by more than five percentage points in a month, a Herald-DigiPoll survey has found.
But National is still popular enough to govern without support parties.
And John Key's popularity as preferred prime minister has risen.
The gap between the two main parties is now 15.1 percentage points, down from 20.7 points in last month's poll just after the Budget.
Labour's support rose 2.4 points to 36.1 per cent and National's fell by 3.2 to 51.2 per cent of decided voters.
Undecided voters totalled 11.2 per cent of those polled, similar to the 11.6 per cent last month.
If the results were translated to seats in the House, National would have 63 MPs in a Parliament of 123, giving it an outright majority.
National now leads a minority Government with 58 of the votes in the 122-seat Parliament. It also has Act's five votes and the Maori Party's four votes on confidence issues.
Act has barely budged in the poll standings, up to 1.9 per cent from 1.7 per cent, despite the Don Brash leadership coup in April, and it would be entitled to only two MPs if it retained the Epsom electorate.
Green Party support is above the 5 per cent threshold at 6.6 per cent, but New Zealand First, which failed to reach the threshold at the last election, fell 1.5 points to 1.2 per cent.
Hone Harawira's new Mana Party has registered support for the first time with 0.5 per cent of the party vote, which is not enough to bring any other MPs into Parliament with him.
Although National's support has dropped, backing for Mr Key as preferred prime minister has risen from 67.7 per cent last month to 70.6 per cent of decided respondents.
The proportion of voters who believe the Government is heading in the right direction rose from 52.8 per cent last month to 56.8 this month.
Those who don't believe it is moving in the right direction fell from 37.5 per cent to 35.2 per cent.
A breakdown of the party vote suggests Labour's support has improved among Auckland voters and younger voters compared to the Herald-DigiPoll survey.
Support for Labour in Auckland at 40.5 per cent is higher than its overall party-vote support.
And its support in the 18 to 39 age group is at 42.3 per cent, again a lot higher than its overall party-vote total.
Five months before the last election, National was polling 54.9 per cent and it eventually won 44.93 per cent of the vote.
Labour was polling 32.4 per cent and won 33.99 per cent.