The number of employed Australians rose by a further 27,900 in July, disguising a sharp drop in full-time employment.
Figures released on Thursday showed full-time employment fell by 20,300 in July, partly offsetting a 48,200 surge in part-time employment.
The jobless rate was 5.6 per cent after an upwardly revised 5.7 per cent in June.
Economists say strong employment growth is needed to lift wages growth.
Figures on Wednesday showed overall annual wage growth remained at a 20-year low of 1.9 per cent and private sector outcomes were even more benign at 1.8 per cent over the year to June, just below the consumer price index at 1.9 per cent.
The May budget forecast wages to rise two per cent in 2016/17, 2.5 per cent in 2017/18 and 3.75 per cent by 2020/21.
Asked if he was still confident of that outlook, federal Treasurer Scott Morrison said "we'll update those if they need to be updated".
"I don't share the view that the Australian economy and wages won't lift in the future, particularly if we continue to make the good choices we are making around the economy," he told ABC radio on Thursday.
Labor finance spokesman Jim Chalmers said the headline jobless figure had been "roughly stable" since the coalition came to office.
"Underneath the headline with those seasonally adjusted numbers, 20,000 less full-time jobs is very concerning," he told Sky News.
Mr Chalmers was also concerned there were 14 million fewer hours worked in the economy over the month.
"The story there is about under-employment - we've got 1.1 million Australians who want to work more and can't find more hours."