* Investors waiting for U.S. CPI on Tuesday

* Fed expected to skip rate hike this week

* Oil slides around 2% over China worries

LONDON, June 12 (Reuters) -

European shares rose on Monday and world stocks were just below recent 13-month highs ahead of key U.S. inflation data on Tuesday, which investors expect to show inflation cooling, and U.S. Federal Reserve and European Central Bank meetings later in the week.

Market sentiment picked up in early European trading after a cautious Asian session. Wall Street futures were up, pointing to another session of gains after the S&P 500 rose for the fourth week in a row last week.

At 1205 GMT, the MSCI World Equity index was up 0.1% on the day, holding just below a recent 13-month high, while MSCI's Europe index was up 0.6%.

Europe's STOXX 600 was up 0.3% and London's FTSE 100 was up 0.1%.

Nasdaq e-minis were up 0.5% and S&P 500 e-minis were up 0.3%.

Investors are waiting for U.S. CPI data due on Tuesday.

"Inflation is really moving in the right direction in Europe, and everyone’s hoping that this is going to be confirmed also in the U.S. tomorrow," said Samy Chaar, chief economist at Lombard Odier, describing markets as in "wait-and-see mode."

"Obviously if we have a big negative surprise on inflation and inflation comes in much hotter than expected, that is going to challenge central banks and the Fed in its 'pause' strategy," he said.

Investors expect the Fed to keep rates steady when its two-day meeting ends on Wednesday, but surprise rate hikes by the Reserve Bank of Australia and the Bank of Canada last week raised the possibility that central banks will prolong their tightening cycles.

Money markets are pricing in around a 75% chance of the Fed keeping rates steady, and a 25% chance of a 25 basis points rate hike, according to the CME FedWatch tool.

The U.S. dollar index was down 0.1% on the day, at 103.44 .

The euro was up 0.2% at $1.0766. The European Central Bank is expected to raise rates by 25 basis points on Thursday.

Euro zone government bond yields slipped, with the benchmark 10-year German yield down 2 basis points, at 2.357%.

Germany's two-year government bond yield, which is sensitive to interest rate expectations, was down 3 bps at 2.947% .

The Bank of Japan is due to deliver its rate decision on Friday and is expected to maintain its ultra-loose policy. Japan's wholesale inflation slowed for the fifth month in a row in May, data showed.

China's weak post-COVID economic recovery continued to weigh on sentiment, and Chinese and Hong Kong stocks fell.

Investors are focusing on the rate at which the People's Bank of China (PBOC) will roll over a batch of 200 billion yuan ($28.00 billion) worth of medium-term policy loans, which are due to mature on Thursday.

A cut, which is possible given China's post-pandemic recovery has begun to sputter, would increase the gap between U.S. and Chinese rates and could weigh on the yuan.

Oil prices fell, as concerns about lower fuel demand from China and rising Russian crude supply weighed on the market.

Brent crude futures fell 1.9%, to $73.36 a barrel and U.S. West Texas Intermediate (WTI) crude was at $68.58, down 2.3%.

(Reporting by Elizabeth Howcroft; Editing by Sharon Singleton and Chizu Nomiyama)