* Euro STOXX 600 down 0.5%

* U.S. futures dip after holiday; oil erases some gains

* Nikkei down 0.3%

* Graphic: World FX rates http://tmsnrt.rs/2egbfVh

* Graphic: Global asset performance http://tmsnrt.rs/2yaDPgn

LONDON/SYDNEY, July 5 (Reuters) - Global shares fell on Wednesday as fresh signs of China's faltering economic recovery emerged, with traders awaiting U.S. Federal Reserve minutes and a key U.S. jobs report later in the week for clues to the central bank's rate outlook.

In quiet trade following the Independence Day holiday on Wall Street on Tuesday, European stocks slipped 0.6%, with German shares down the same amount.

Wall Street was set for losses, too, with S&P 500 futures and Nasdaq futures down 0.2%-0.4%.

The Chinese services sector, which has rebounded strongly since the lifting of COVID-19 lockdowns, expanded at the softest pace in five months in June, a survey showed, adding to signs of a soft recovery in the world's second-biggest economy.

The release of the minutes of the Fed's last policy meeting, due later on Wednesday, and the non-farm payrolls report on Friday are top of traders' agenda this week as they watch to see whether the Fed will need to hike more than once to stem inflation.

"Focus is very much on whether is inflation peaking; has it peaked; how many more rate hikes are coming down the hike?" said Michael Hewson, chief market analyst at CMC Markets.

The MSCI world equity index, which tracks shares in 47 countries, fell 0.2%.

Markets are almost certain that the Fed will hike in July after pausing last month, but have only priced in a 32% chance that it would need to deliver another hike by October.

The U.S. jobs data is also key, traders say.

Economists polled by Reuters expect the United States to have added 225,000 jobs last month, slowing from 339,000 in May, while the growth in average earnings likely held steady at 0.3% from the previous month.

"It's almost a race about whether inflation will fall quickly enough to allow the policymakers to back off before the growth dynamic moves into recession," said Guy Miller, chief market strategist at Zurich Insurance Group.

The U.S. dollar drifted near the middle of its range of the past three weeks against major peers, with the dollar index down 0.1% to 102.99, after tracking between 103.75 and 102.75 since early June.

Earlier, MSCI's broadest index of Asia-Pacific shares outside Japan dropped 0.7% after the China data. Japan's Nikkei also fell 0.3% on profit-taking after climbing to three-decade highs.

Chinese blue chips fell 0.8% and Hong Kong's Hang Seng index sank 1.6%.

MUTED MOVES

Elsewhere in the currency markets, moves were largely muted. The yen edged up 0.1% to 144.59 per dollar, just a touch below 145.07, which was its weakest in eight months as fears of official intervention took hold.

Short-term Treasury yields eased 2 basis points to 4.9215% while 10-year yields were little changed.

The euro edged 0.2% higher to $1.0898, adding to its 0.34% overnight decline.

Oil prices gave up some of their gains on Wednesday after advancing on supply concerns stemming from production cuts by top producers Saudi Arabia and Russia.

Brent crude futures fell 0.2% to $76.05 a barrel after climbing 2.1% overnight.

(Reporting by Tom Wilson in London and Stella Qiu in Sydney Additional reporting by Dhara Ranasinghe Editing by Sam Holmes and Helen Popper)