The figures for the year to May showed 10,379 homes were consented in Auckland.
Auckland Council has estimated the city is growing by 45,000 residents a year and around 14,000 new homes a year are needed to meet demand.
"Auckland accounted for three-quarters of national new apartment units and nearly half of all townhouses, flats, and units," said prices, accommodation, and construction senior manager Jason Attewell.
Auckland's increases in these home types were partly offset by a fall in the number of new stand-alone houses in Auckland in the latest year.
"Annual new home numbers are nearing those last seen in 2004, although they remain well below the all time peak of the mid-1970s when consents reached about 39,000 a year," he said.
Westpac senior economist Satish Ranchhod noted that data did include a positive trend towards an increase in multi-unit consents (such as apartment and townhouses).
But it was "still below what is needed to keep up with population growth," he said.
"With increasing reports of capacity constraints in the building industry, this signals that the supply shortfall in Auckland is likely to get worse before it gets better.
ASB economist Jane Turner noted that consents "can be volatile month to month, and this was particularly evident in consents for town houses, which lifted strongly in May and fell back in June".
"But looking beyond the volatility, we are seeing encouraging signs that residential building demand is lifting in Auckland and Wellington."
New home consents rose significantly in Otago (up 28 per cent), and Wellington (up 20 per cent) regions in the June 2017 year, but fell 20 per cent in Canterbury to 5180.
New home consents issued in Canterbury have been falling for the past two years, as they come off the post-2011 earthquake residential rebuild peak of almost 7000 in the June 2015 year.
Research released by Statistics NZ last month showed that about 97 per cent of dwelling consents lead to a home being finished. But there was a delay of at least 10 months between consents issued and building getting underway.
That combination meant that just 8600 houses were actually built in the Auckland area in the past year.