May 13 (Reuters) - Australian shares inched lower on Monday, with banks declining the most followed by energy stocks, while investors awaited U.S. inflation data and local employment data due later this week for hints on the central bank's next interest rate moves.

The S&P/ASX 200 index fell 0.3% to 7,726.0 by 0033 GMT. The benchmark closed 0.4% higher on Friday.

Globally, investors are awaiting the U.S. core consumer price index based inflation data, the Federal Reserve's preferred measure of inflation, due on Wednesday for clues on when the central bank might start cutting interest rates.

Markets are now pricing in a 61.2% chance of the Fed cutting interest rates in its September meeting, compared to a 76.2%, a month ago, according to CME FedWatch Tool.

Back in Sydney, investors will be looking at local employment data for April, due on Thursday, which could influence the Australian central bank's rate trajectory for the year.

Rate sensitive financials led losses on the benchmark, dropping 1.04%, with National Australia Bank , Westpac and ANZ Group falling between 0.1% and 3.7%.

Energy stocks fell 0.9% on declining oil prices, as comments from U.S. central bank officials indicated higher-for-longer interest rates.

Sector heavyweights Woodside and Santos were down 0.6% and 0.8%, respectively.

Real estate stocks slipped 0.6%, with Charter Hall Group and Goodman Group falling 0.2% and 0.1%, respectively.

However, the mining sector gained 0.1%, with mining behemoths BHP Group, Rio Tinto and Fortescue adding between 0.2% and 0.8%.

Among other sectors, gold stocks rose 0.5% while information technology firms gained 0.3%.

In New Zealand, the benchmark S&P/NZX 50 index dropped 0.6% to 11,688.87, with investors awaiting the Reserve Bank of New Zealand's monetary policy decision due next week.

(Reporting by Roshan Thomas in Bengaluru; Editing by Rashmi Aich)