SYDNEY (Reuters) - A private-sector gauge of Australian consumer prices fell in May, indicating a lack of inflationary pressure that could keep the door open for another cut in interest rates.

The Melbourne Institute monthly inflation gauge fell 0.2 percent in May, from April when it rose 0.1 percent.

That slowed the annual inflation rate to 1.0 percent, from 1.5 percent, driving it further below the Reserve Bank of Australia's (RBA) 2 percent to 3 percent target band.

The trimmed mean measure also dipped 0.2 percent, reversing a 0.2 percent rise in April. In the twelve months to May, the trimmed mean increased by 1.0 percent, down from 1.5 percent.

"This month, the result was driven by falls in fruit and vegetable prices, as well as falls in non-durables and international holiday travel," said Sam Tsiaplias, senior research fellow at the Melbourne Institute.

"Looking at either the headline or trimmed mean measures, annual inflation appears to have fallen to about 1 percent. Inflation excluding volatile items has also fallen to 1.5 per cent in annual terms. Whichever measure happens to be preferred, it is fairly clear that there is a sizeable gap between target and actual inflation."

The RBA holds its monthly policy review on Tuesday but is unlikely to deliver a back-to-back cut to the cash rate, which is already at a record low 1.75 percent.

(Reporting by Ian Chua; Editing by Sam Holmes)