By Stella Qiu

SYDNEY (Reuters) - Australia's consumer inflation slowed to a 13-month low in May, driven by a sharp pullback in fuel, while a measure of core inflation also cooled in a sign interest rates might not have to rise again in July.

Data from the Australian Bureau of Statistics on Wednesday showed its monthly consumer price index (CPI) rose 5.6% in the year to May, marking the smallest increase since April last year.

That was down from 6.8% the previous month and well below market forecasts of 6.1%.

On a monthly basis, CPI fell 0.4% in May. The core trimmed mean measure of CPI rose by an annual 6.1%, a seven-month low and again down from 6.7% in April.

Investors responded by pushing the Australian dollar down 0.8% to $0.6632, while markets moved to price in a lower chance of a hike in July, with a 30% probability, and wagered that rates are more likely to peak at 4.35%, rather than 4.6%.

The Reserve Bank of Australia has raised interest rates by a whopping 400 basis points to 4.1% since May last year, but the upside risks to inflation meant the central bank has adopted a hawkish tone in recent months, warning that more rate rises may be required.

"The number is at the very lower end of the range of economists' expectations which ranged from 6.9% to 5.6% and is soft enough by a good margin to see the RBA halt its series of rate hikes in July and possibly beyond," said Tony Sycamore, market analyst at IG.

Wednesday's data showed the most significant drivers were an 8.4% jump in housing and a 7.9% increase in food and non-alcoholic beverages. Offseting the rise was an 8.0% drop in automotive fuel prices.

Working against the odds of a pause next week, a closely watched measure of prices excluding volatiles and holiday travel slowed just marginally to 6.4% from 6.5%, and a blockbuster jobs report had raised stakes for further rate rises.

"With the labour market still very tight, unit labour cost growth surging and the housing market bouncing back with a vengeance, we suspect that the Bank will press ahead with another rate hike next week," said Marcel Thieliant, a senior economist at Capital Economics.

(Reporting by Stella Qiu; Editing by Sam Holmes)