But rents fell in Christchurch, where Infometrics said there was an oversupply of housing, Rents were down there 5.9 per cent in the past 12 months and 13 per cent in total since September 2014.
Otago rental inflation rose to a 12-year high due to growth in Dunedin, Infometrics said.
The Central Otago and Queenstown-Lakes markets showed signs of slowing but were up 8.5 per cent and 8.4 per cent per annum.
Rental inflation in Upper Hutt and Lower Hutt was at nine-year highs.
But in the Auckland metropolitan area - which excludes Rodney and Franklin - rents were up only 3.3 per cent per annum, the report said.
"The sheer size of the rental market in Auckland means that its softening, along with some easing in Bay of Plenty, has been sufficient to offset the strength of rents in other parts of the country.
"Even with house price inflation having slowed in Auckland, the lack of rental growth has meant little improvement in yields to date. In fact, yields in the old Auckland City area have fallen to a new record low, as have yields nationally."