An economist says the unemployment rate could move back up towards the 7% mark for the June quarter.
The ANZ Bank's monthly job advertisements survey shows, on a seasonally adjusted basis, the number of jobs advertised online and in newspapers was unchanged in June compared with May, when there had been a 1.4% fall.
The unchanged total reflects a 0.5% increase in internet advertising, however, this was offset by a 2.5% fall in newspaper ads.
On an annual basis the index is just 0.7% higher compared with June last year, while internet advertising is up 3% for the same period.
ANZ senior economist Sharon Zollner says there's a risk that the sharp improvement in the unemployment rate in the first quarter of the year might be reversed.
She says job ads tend to lead what is happening in unemployment by a few months and the latest figures are not indicating a rapid improvement in the labour market any time soon.
Ms Zollner says that's surprising given that confidence amongst consumers and businesses has improved and although businesses have been saying they intend taking on more staff they don't seem to be following up on that.
"I think it maybe paints a picture of some weariness on the part of businesses, basically it's been a pretty hard slog ever since the recession, per capita GDP is still lower than it was in 2007 so firms are just waiting to be totally sure that this upswing is for real before they take on new staff, I think."
Official labour market data for the June quarter is due on 7 August.