Worries that Australia’s unemployment rate could rise above 6.5 per cent over the next year may have been temporarily doused, according to minutes from the most recent meeting of the Reserve Bank board.

The board appears to be positive about the direction of the jobless rate, which rose only slightly from a revised 5.9 per cent in May to a steady 6 per cent in June.

The minutes cite recent data from the Bureau of Statistics which it said showed, “further signs of improvement in May”, and that employment growth had picked up over the year to exceed the rate of population growth in Australia.

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“As a result, the unemployment rate had been relatively stable since the latter part of 2014,” the minutes noted.

“Demand for labour could be sufficient to maintain a stable or even falling unemployment rate in the near term.”

However, the board warns that other forward looking indicators suggest “only modest growth” for employment in the coming months.

Jobs growth has been strongest in household services and employment opportunities have also been growing in business services, though little changed in the goods sector.

However, despite the optimism about the labour market, the minutes cite national accounts data that show non-farm average earnings per hour are at their lowest level since the early 1990s, while unit labour costs were little changed in four years.

The falling population growth rate has been put down to falling immigration, which was noticeable in Western Australia and Queensland because of the fading mining investment boom.

The minutes show that non-mining business investment remains subdued and that surveys of business investment intentions suggest it will remain that way over the coming year.

The RBA was assessing unfolding events in Greece at the time of the meeting, but judged that any potential fallout in Australia was “relatively limited”.

The Reserve Bank is also continuing to monitoring the impact of booming property prices in Sydney and to a lesser extent Melbourne, but said the scrutiny of investor lending by the banking regulator APRA is yet to become evident.

The RBA is also watching the direction of the Australian dollar and repeated that “a further depreciation is both likely and necessary.”

The Australian dollar has been sitting below 74 US cents in recent days and was trading relatively stead at 73.65 US cents at 11:39am (AEST), shortly after the minutes became public.

The Reserve Bank left the cash rate on hold at its July 7 meeting saying that, while the decision was “appropriate”, it would be assessing economic and financial information in the coming months before reconsidering the outlook for monetary policy.