Commonwealth Bank of Australia said Friday it expects Australia's annual headline inflation to soften slightly to 4.1% in May from 4.2% in April due to lower fuel prices.

But despite lower fuel costs, underlying inflation will probably remain "too high," keeping the Reserve Bank of Australia on alert, Commonwealth Bank said.

It added that there is still a lot of uncertainty around the extent to which businesses pass higher costs on to consumers, even after cost pass-through in April remained broadly limited.

"While we expect some increase in pass-through during May, the available data suggest that the more severe inflation scenarios considered in the immediate aftermath of the Middle East conflict have so far not materialized," the bank said.