* Euro zone private business growth slows
* France contracts, Germany bounds ahead
* Chinese factory activity improves but still contracting
* Japan shows similar trend, but export orders weaken
* U.S. data expected to show slight pick up
By Jonathan Cable and Koh Gui Qing
LONDON/BEIJING, May 22 (Reuters) - Private business activity in the euro zone grew at just under its fastest pace in three years this month, while contraction in China's vast manufacturing sector slowed to its weakest pace this year, surveys showed on Thursday.
But in Europe, only drastic price cuts helped stop a further slide, after a sharp slowdown in factory growth took the shine off an unexpected pickup in the service industry. The slowdown kept alive worries about dangerously low inflation.
"Overall, the data is a bit of a relief after disappointing first quarter figures," said Christian Schulz, senior economist at Berenberg Bank.
"In China, the authorities are doing something and the economy is responding. (But) the European Central Bank is worried because it looks like inflation will stay low for a long period of time."
Markit's Composite Purchasing Managers' Index for the currency bloc, seen as a good indicator of growth, edged down to 53.9 from a near three-year high of 54.0 in April, matching the consensus forecast in a Reuters poll of analysts.
Readings above 50 indicate expansion, and Markit said the index pointed to second-quarter economic growth of 0.5 percent, which would be the strongest in three years, and better than the 0.3 percent predicted in a Reuters poll on Wednesday.
European stocks and government bonds rose after the data were released on Thursday.
But the data also revealed the biggest split between the euro zone's two largest economies since February. France contracted while Germany bounded ahead, although led by services rather than manufacturing.
Decent overall growth is good news for the ECB, but with official inflation running at 0.7 percent, well below its 2 percent ceiling, it will be concerned that companies slashed prices for the 26th month running to drum up trade.
The ECB is expected to cut what little it has left of its main interest rate and push the deposit rate below zero next month, a Reuters poll predicted this week.
"Today's data are a reminder of the fragility and unevenness of the recovery. With inflation low and a sustained euro zone recovery not yet assured, further ECB easing in June looks all but certain," said Martin van Vliet at ING.
The economic picture was also mixed for the world's second-largest economy, China.
HSBC/Markit's Flash China Manufacturing PMI rose to 49.7 in May from April's 48.1, reaching its highest since December and beating the median forecast of 48.1 in a Reuters poll.
Sub-indexes measuring output as well as domestic and foreign demand all recovered sharply. But factory jobs were shed for the 13th month and the overall index was still pointing to contraction.
Premier Li Keqiang said in March it was acceptable for GDP growth to be slightly below the 7.5 percent target this year as long as the job market held up. Previously, he has said growth of at least 7.2 percent was needed to create sufficient jobs.
But just as China and the ECB look set to ease policy the Bank of England is increasingly becoming the hot favourite to be the first major central bank to begin hiking interest rates - probably in the second quarter of next year.
Official data earlier on Thursday confirmed Britain's economy grew 0.8 percent last quarter as households spent more and companies increased investment at the fastest pace in a year.
Federal Reserve policymakers last month also began laying groundwork for an eventual retreat from easy monetary policy with a discussion of how to best control interest rates as they remove trillions of dollars from the financial system.
But any tightening is still some way off. A survey due from the United States is expected to show manufacturing activity picked up a tad this month.
A similar survey showed Japanese factories had contracted slightly in May but at a slower pace than in April, suggesting some recovery from the impact a sales tax increase last month.
The Markit/JMMA flash Japan Manufacturing PMI rose to a seasonally adjusted 49.9 in May from April's 49.4.
Editing by Kim Coghill, John Mair and Janet Lawrence