Log, apple and skim milk powder prices all gained 2 per cent, while processed timber rose 1 per cent.
Prices for lamb, wood pulp and venison were unchanged, according to the index.
ANZ said dairy prices, which underpin the index with a 43 per cent weighting, fell 4 per cent in June - the fifth consecutive monthly fall.
Dairy prices have dropped to their lowest level in almost three years, 31 per cent below their last peak.
ANZ said a resurgence in the New Zealand dollar, which was trading at US80.54c late yesterday against the greenback, was compounding the fall in commodity prices.
The rising value of this country's currency drove a 3.4 per cent drop in the NZ dollar commodity price index to a level not seen since October 2009, the bank said.
ANZ economist Steve Edwards said it would take "a bit of certainty" about the direction the global economy was heading in to reverse the downward trend in prices.
"[The drop in prices] is definitely reflecting the uncertainty out there," Edwards said. "It's hard to say how much further it might drop."
New Zealand was benefiting from continuing strong growth in Asian economies.
"As long as Asia hangs in there we should be okay, but if Asia gets sucked into the vortex it could be quite disastrous," Edwards said.
Weakening Chinese manufacturing data has raised concerns that growth is slowing in the world's second largest economy.
BNZ economist Doug Steel said the drop registered in the June commodity price index was as expected, given the slowdown in global economic growth.
"There's nothing too alarming in it," Steel said. "From a policy perspective I don't think the Reserve Bank will see any surprise in it."
He said the combination of falling commodity prices and strengthening dollar was "certainly a negative" for New Zealand's current account balance - the difference between what the country earns and spends overseas - which was expected to plunge further into deficit over the next 12 months.
Like Edwards, he said it was difficult to pick exactly how long the downward trend in commodity prices might last.
"Obviously a lot is riding on what happens in Europe and world growth generally," Steel said. "Our core view is that [commodity] prices, while they might remain volatile for the foreseeable future, could average around current levels through the second half of the year."
Edwards said prices for so-called soft commodities like dairy did not tend to get as badly affected by a downturn in global economic conditions as other commodities, such as oil.
Benchmark Brent crude hit an 18-month low of US$90.62 a barrel last month.
"People still need food on their table to eat," Edwards said. "Longer term, the picture's good for New Zealand, we've just got to weather this storm at the moment."
