The increase in Australia's jobless rate adds to the case for the Reserve Bank of Australia (RBA) to hold off on hiking interest rates again, Commonwealth Bank of Australia (ASX:CBA) said in a Friday note.

The country's seasonally adjusted unemployment rate increased to 4.5% in July from 4.4% in the previous month as employment fell by 15,800 people, data from the Australian Bureau of Statistics (ABS) showed. Wages data for the June quarter showed private sector wages grew 0.7%, the slowest pace since 2021.

The fall in employment was well below consensus forecast for a rise of 12,000 jobs. Together, both data were consistent with a gradual softening in the labor market.

"Overall, the data is supportive of our view that the labor market remains on a solid footing but is slowly loosening and is moving closer to balance. Over time, this should assist in bringing inflation down and supports the case that interest rates have peaked this cycle," according to CBA economist Harry Ottley.

The ABS cautioned that a smaller sample size in the July survey meant "the standard errors on estimates are bigger" and fluctuations should be taken with a grain of salt.