The jobless rate jumped from 3.4 per cent in the March quarter, according to a Stats NZ release on Wednesday, just a tick above market expectation.
An aggregate of bank economists and the Reserve Bank believed the figure would come in at 3.5 per cent.
The jobless figure continues to crawl upwards from basement lows of 3.2 per cent in late 2021, and corresponds with the Reserve Bank's interest-rate hiking phase which began at that time.
While the jobless rate ticks up, a record number of New Zealanders are in work, as measured by the labour force participation rate.
That figure hit 72.4 per cent - a record since the series began in 1986 - and can indicate full-time students or retired people picking up jobs.
The employment rate for women is at an all-time high of 65.4 per cent.
The number of people not in the labour force fell by 10,000 Kiwis to 1.15 million.
Stats NZ spokeswoman Becky Collett said tourism businesses - such as hotels, travel agencies, sightseeing operators and cafes - were putting more Kiwis in jobs.
"Despite its small size, a quarter of all annual employment growth was recorded in key tourism-related industries," Ms Collett said.
On the same day, Stats NZ released data on wage cost inflation, which was steady at 4.3 per cent in the year to June.
Average ordinary time hourly earnings have grown 6.9 per cent to $NZ39.53 ($A36.69).