Construction costs rose 1.7 per cent in the quarter. For the year they are up 4.1 per cent, driven by a 12 per cent rise in Christchurch.
Electricity rose 2.6 per cent, making 3.4 per cent for the year.
The rise in house prices (which are not included in the CPI) has yet to show up in rents, which rose 0.4 per cent in the quarter (0.6 per cent in Auckland) and 2.1 per cent over the year.
Some economists have pointed to relatively low increases in rents to question the widespread claim that there is a severe housing shortage, and concluded instead that there is a speculative element.
Like the lower dollar, the recent rise in petrol prices came too late to make much difference to the June quarter inflation outcome. Petrol fell 2.4 per cent in the quarter to be down 2.8 per cent for the year.
ANZ economist Mark Smith said yesterday's data had something for both hawks and doves.
Doves could point to the fact that it is the seventh time in eight quarters that inflation has come in below Reserve Bank forecasts, that retail discounting is widespread, and core inflation measures are low across the board.
"Hawks can point to the fact that construction cost inflation in Canterbury is running at nearly 12 per cent per annum and is rising everywhere. They can also point to ongoing increases in dwelling insurance costs given the shift to sum-insured policies [from full replacement]."
Insurance costs rose 2.4 per cent in the June quarter.
In the September quarter higher fuel prices alone would raise the CPI by 0.3 per cent, Smith said.
AMP chief economist Bevan Graham also expects inflation to head higher, reflecting both a lower dollar and stronger economic growth.
ASB economist Jane Turner said the low rate of current inflation would continue to hold the Reserve Bank back from using interest rates to cool the housing market, at least until the March quarter next year.
Instead restrictions on high loan-to-value ratio lending are highly likely, she said.