* European stocks down on U.S. inflation uncertainty

* China property fears weigh on sentiment

* Australia central bank says worst over for inflation

LONDON, Aug 11 (Reuters) -

European stock indexes fell in early trading on Friday after data showed U.S. consumer prices increased moderately in July, which kept investors cautious ahead of more U.S. numbers later in the session.

The consumer price index rose

0.2% last month

, the same increase as in June, prompting initial relief in markets on Thursday as some saw the data as lessening the chance of another Federal Reserve rate hike next month.

Investor optimism was kept in check by San Francisco Federal Reserve Bank President Mary Daly saying that

more progress was needed

before she would feel comfortable the Fed has done enough to combat inflation.

Asian stocks fell to

a one-month low

and European indexes were in the red, with the STOXX 600 down 0.7% at 0924 GMT.

The MSCI World Equity index was down 0.3% on the day, set for a small overall weekly decline.

Investors were waiting for U.S. producer price and consumer sentiment data due later in the session.

"We’re still getting a mixed message from the inflation numbers," said Ben Laidler, global markets strategist at eToro.

"Hopefully (today's data) confirms the message we got yesterday which is a little bit of breath of relief that inflation’s not picking up more, and the underlying trend remains easing inflation."

In Australia, the head of the central bank said policy was in the

"calibration stage"

as the worst was over for inflation, though some further policy tightening might be needed depending on incoming data and evolving risks.

Weak data from China was also weighing on sentiment, eToro's Laidler said. Data on Wednesday pointed to deflation in China, adding to fears that it is entering an era of much

slower economic growth

akin to the period of Japan's "lost decades".

Chinese property companies were taking a

fresh beating

. Giant developer

Country Garden

slid to a record low after forecasting a $7.6 billion net loss in the first half.

The dollar was broadly steady, with the dollar index at 102.58, on track for its fourth weekly gain in a row.

The stronger dollar was instrumental in the yen touching a six-week low of 144.89 per dollar in early trade, though volumes were thinned owing to a public holiday in Japan.

Euro zone bond yields rose, with Germany's benchmark 10-year yield up around five basis points at 2.574%.

The euro was steady at $1.0981.

The pound was up 0.2%, after

GDP data

showed Britain eked out some unexpected growth in the second quarter, helped by a strong June performance. But it remains the only large advanced economy yet to regain its pre-COVID late-2019 level, data showed on Friday.

Investors will be watching for UK inflation data next Wednesday.

Oil prices held near recent highs, with Brent crude down 0.4% at $86.07 and West Texas Intermediate crude futures down 0.4% at $82.48.

The International Energy Agency (IEA) said

demand growth for oil

next year will be slower than previously forecast, citing lacklustre macroeconomic conditions, a post-pandemic recovery running out of steam and the burgeoning use of electric vehicles.

(Reporting by Elizabeth Howcroft; editing by John Stonestreet)