The Reserve Bank has forecast a 0.5 per cent gain over the quarter.
BNZ economist Doug Steel said recent weak manufacturing data pointed to a slowdown, but that it was too early to cry "recession" just yet.
"It's been slowing down for some time and I think that this week's data will just confirm that," Steel said.
"It doesn't mean that the economy will do anything more than that - we are not talking about recession here," he said.
"We are still seeing growth, but that growth will be slower than it has been," Steel said.
BNZ expects a 0.3 per cent increase in GDP over the June quarter, for an annual quarter-on-quarter gain of 1.9 per cent.
ANZ senior economist Miles Workman said economic growth had been "running out of puff" for a while now.
"Forward-looking indicators suggest this process has continued into Q3, which, alongside a softening pipeline for construction activity, some worrying signals for employment growth, a persistently pessimistic business sector, and an increasingly fragile global backdrop, means the medium-term outlook is looking less assured," Workman said in a research note.
"That said, despite all the negative developments in recent months, we're still of the view that there will be enough supports out there to eventually put a floor under the slowdown and prevent growth from rolling over: Monetary conditions are, and will remain, accommodative," he said.
ANZ expects to see a 0.4 point gain over the quarter, which would see the annual growth rate slow to about 2.0 per cent - the softest pace since the fourth quarter of 2013.
Workman expects the Reserve Bank to use all of its "conventional" ammunition by cutting the official cash rate to just 0.25 per cent by May, 2020.
The rate, which comes under review on September 25, sits at 1.0 per cent after the Reserve Bank surprised the market with an unexpectedly large 50 basis point cut in August.
Westpac sees a 0.6 per cent rise in GDP for the June quarter, matching the pace seen in the previous two quarters and slightly ahead of the Reserve Bank's forecast.
"That wouldn't be a great result – the pace of growth is clearly down from the highs seen in 2016 and 2017 – but it would at least suggest that there hasn't been a further deterioration so far this year," Westpac said.
"We expect GDP growth to remain subdued in the second half of this year. While there is already substantial monetary and fiscal stimulus in place, we think it will take some time for this to have an impact on households' willingness to spend," Westpac economists said.
In June quarter balance of payments data due on Wednesday, ANZ expects the current account deficit to narrow slightly to 3.4 per cent of GDP.