Net core Crown debt dropped slightly from the previous month at around $101b, but was around $6b below forecast.
Treasury said "almost all key metrics" were more favourable than those set out in the Budget.
In a statement chief government accountant Paul Helm said corporate tax, source deductions (such as PAYE) and GST were all ahead of forecast.
"These positive variances reflect economic conditions being better than forecast," Helm said.
"Labour market conditions were better than forecast which has driven the positive variance in source deductions and consumption was also stronger, leading to GST revenue being higher compared to forecast."
May's Budget assumes the Crown would run a $15.1b deficit in 2021, rising to $18.4b in 2022, before a series of smaller deficits during the forecast period.
Finance Minister Grant Robertson said the figures show "the economy's resilience and New Zealanders' confidence in the recovery" but warned the outlook remained uncertain.
"The recent case of an Australian traveller in Wellington with Covid-19, Australia's growing outbreak and the pandemic more globally shows the economic environment remains volatile. The recovery remains uneven among some sectors and regions in New Zealand, while supply chain issues still affect the economy."
The full year accounts will not be released for several months.