The latest jobs figures have helped to take the edge off recent negativity shrouding Australian financial markets caused by global worries over Greece and China.
Employment Minister Eric Abetz believes there are "green shoots" in the economy that are blossoming into new jobs.
A modest 7300 jobs were added to the workforce in June, building on the 40,000 jump in the previous month.
At six per cent, the jobless rate was better than the 6.1 per cent expected by economists, albeit coming off a downwardly revised 5.9 per cent in May.
It was the first time unemployment had been below six per cent in just over a year.
"It is reassuring to see the unemployment rate relatively stable yet again with more jobs being created," Senator Abetz told reporters in Hobart on Thursday.
He said the government is rolling out new infrastructure and has signed free trade agreements with "huge job growth potential".
Labor's employment spokesman Brendan O'Connor said the jobless rate was still too high and the government should be focusing on a credible plan to tackle unemployment.
Instead it is spending $80 million on a trade union witch-hunt, he said in reference to the royal commission where Opposition Leader Bill Shorten has been giving evidence.
"(Senator) Abetz should spend less time exercising his hatred of the union movement and more time on a plan to create jobs," he said in a statement.
The jobs numbers helped the share market recover from an initial sell-off, again dogged by the ongoing worries over sliding equity prices in China and another steep drop in iron ore prices.
Likewise, the Australian dollar rebounded from a six-year low.
It remains to be seen if the data helps to improve consumer confidence after taking a tumble last week on worries that the problems in Greece and China will flow through to the Australian economy.
The modest employment rise in June was the result of a 24,500 increase in full-time employment being partly offset by a 17,200 fall in part-time jobs.
David Lane, a director of business consultants Pitcher Partners, said the move from part-time to full-time employment is positive for the overall health of the economy, and if this trend continues, it should add stability to many parts of the economy.
"This trend may in part reflect an increase in business confidence following the federal budget," he told AAP.
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