The number of new building consents rose by 3.5% in June, after falling by 9.5% in May.
Overall, Statistics New Zealand says, there has been a 12% increase in the number of residential building consents issued in the last year.
Excluding apartments, the number of housing consents for the year ending in June rose 25% compared to last year.
However the figures show this is the second lowest annual total for a June year since record-keeping began in 1991.
ASB economist Jane Turner says the data shows demand for housing remains very weak and points to a subdued recovery in residential construction.