Total construction work completed during the June quarter rose by a smaller-than-expected 0.8 per cent, with the residential building sector surprisingly going backwards.
Economists had expected a 2.8 per cent rise in the quarter.
Total construction rose to $52.9 billion in the June quarter to be up 0.4 per cent on the year.
Total building construction rose 0.1 per cent to $30.6 billion, but residential building declined 0.1 per cent in the quarter to $19 billion, although was still 8.9 per cent higher than a year earlier.
Economists had expected another strong result for housing construction, given ultra-low interest rates and the lingering impact from the federal government's HomeBuilder program.
Non-residential contraction did rise 0.3 per cent in the June quarter to $11.5 billion, but was still down six per cent compared with a year ago.
Engineering rose 1.8 per cent to $22.3 billion.
The data feeds into the national accounts for the June quarter due next Wednesday.
Much of the recent focus has been on Australia's economic performance during the September quarter because of the current spate of virus lockdowns and whether an expected downturn will extend into the December quarter.
Two quarters of economic contraction are classified as a technical recession.
While this makes June quarter figures appear somewhat dated, economists will still be glued to a range of reports in the coming week to see if the economy has already sunk into recession.
The expectation is the economy was already slowing from the rapid recovery seen shortly after last year's recession, and before the current downturn, with economists' growth forecasts for the June quarter ranging as low as 0.2 per cent even before Wednesday's construction data.
Treasurer Josh Frydenberg continues to pin his hopes on a rapid recovery after the widely expected economic contraction in the September quarter.
Treasury and economists are predicting a downturn of between two and four per cent in the September quarter.
"As for the December quarter, I'm hoping that it rebounds strongly off the back of the easing of (coronavirus) restrictions," Mr Frydenberg told the Seven Network on Wednesday.
"We know from our experiences in the economy last year, we rebounded strongly."
But he says the key is to stick to the national plan for COVID-19 restrictions to ease once vaccination rates reach 70 per cent and 80 per cent of the population over the age of 16.
Just over 30 per cent of Australians are fully vaccinated at present.
Australian Industry Group chief executive Innes Willox believes the point has already been reached for governments to look seriously at opening borders and removing barriers to business travellers more rapidly.
"Employers across the country have put investments on hold for too long," Mr Willox said in a statement.
"They are losing business opportunities to their overseas competitors whose economies and countries are open for business, while Australia is locked tight as a drum."
