"Petrol prices rose slowly over the first part of the quarter, reaching a peak in late May and then falling," Stats NZ prices senior manager Paul Pascoe said.
"By the last week of June, the petrol pump price was 2 per cent lower than the June quarter average."
Rental costs were the other driver in an otherwise subdued inflation environment.
Rent prices rose 1 per cent in the June 2019 quarter, and increased 2.5 per cent over the year.
The latest quarterly rise is the largest since the March 2008 quarter when rent prices rose 1.2 per cent.
The Reserve Bank's mandated inflation range is 1 to 3 per cent, and it aims to hit the mid-point of 2 per cent.
The slightly higher inflation figure is unlikely to deter the Reserve Bank from cutting interest rates again this year, economists say.
"Low readings for core consumer price inflation suggest there is a structural (long-lasting) element to the inflation process, which, combined with slowing global growth is unnerving global central banks that are either cutting policy interest rates or seriously contemplating cuts," ASB economists said.
Around the world, inflation has been subdued since the global financial crisis with central banks under more pressure from the risk of deflation.
From late 2014 to late 2016 the New Zealand inflation rate was below one per cent.
The idea that falling prices are a bad thing for an economy can seem counter-intuitive.
But the problem as economists see it - and as witnessed in Japan over the past 20 years - is that when people expect inflation to be consistently low or deflation takes hold this can create a recessionary spiral.
Expectation things will become cheaper suppresses consumer spending and business investment.
The two feed off each other as lower consumption forces businesses to contract and focus on costs. That can start to cost jobs.
