SYDNEY (Reuters) - Australian wages rose at their slowest pace in a year in the June quarter, falling short of expectations, while softer gains in the private sector suggest the labour market was easing.

Figures from the Australian Bureau of Statistics on Tuesday showed its wage price index rose 0.8% in the three months ended June, versus 0.9% in the first quarter and the slowest since the June quarter 2023. That compared with market forecasts for a 0.9% rise.

Annual pay growth held at 4.1%, but past growth was revised up slightly, which means there will be a marked slowdown in the annual rate in the third quarter.

Growth in the private sector rose 0.7% in the quarter, a low last seen in the December quarter in 2021, as the jobless rate ticked up in response to high interest rates.

"The RBA will be somewhat relieved to see wage pressures subsiding," said Sean Langcake, head of macroeconomic forecasting for Oxford Economics Australia.

"However, absent an improvement in productivity growth, the current pace of wage growth is still a little too strong for inflation to return to target quickly."

The Reserve Bank of Australia has held its policy steady since November, judging the current cash rate of 4.35% - up from the 0.1% during the pandemic - is restrictive enough to bring inflation to its target band of 2-3% while preserving employment gains.

However, it judges that the labour market is still running a bit hot, one reason that underlying inflation, which was at 3.9% last quarter, is only expected to return to the target band by the end of 2025.

Some analysts had argued that rates were not high enough, but the RBA's reluctance to hike further has several economists looking for a rate cut early next year, trailing other major central banks.

Markets are now wagering on an easing by the year-end, having only recently implied there was a risk of a further hike.

The overall increase in annual wages was still just enough to take it above inflation of 3.6%, a welcome return to real pay growth after years of negative outcomes.

Incomes will get an added boost from a major round of tax cuts that started in July.

(Reporting by Stella Qiu; Editing by Himani Sarkar)