* China factory activity sinks to 6-1/2-year low
* Orders fall, firms forced to slash output, prices, jobs
* Stocks, commodities fall on global growth fears
* Weak Asian demand drags euro zone private business
* Service firms hike prices for first time in 4 years
By Sumanta Dey and Koh Gui Qing
Sept 23 (Reuters) - The outlook for the global economy became bleaker on Wednesday as signs of a deeper downturn in China emerged, despite massive policy stimulus, coupled with weak growth at best in Europe.
China's vast factory sector shrank at its fastest rate in 6-1/2-years in September, a private survey showed, sending investors worried about sagging global growth scurrying out of risky assets.
Reacting to the data, Asian stocks posted their biggest single-day fall in a month on Wednesday.
Similar surveys, due later on Wednesday, are likely to show the U.S. economy lost some steam in September even with the Federal Reserve holding fire on interest rates.
"There is substantial concern at present that global demand weakness is dampening the economy in the industrial countries," said Jorg Kramer, chief economist at Commerzbank.
The preliminary Caixin/Markit China Manufacturing Purchasing Managers Index fell to 47.0 in September, the worst since March 2009, missing expectations for 47.5 and slipping from August's 47.3. Levels below 50 signify a contraction.
It was the seventh straight month of contraction for the manufacturing sector and the survey showed business conditions deteriorating almost across the board, as firms slashed output, prices and jobs at a faster pace as orders fell.
The data underline the malaise in the world's second largest economy and just how difficult it will be for policymakers to steer the economy out of the biggest downturn in decades.
Last month, Beijing devalued the currency to support exports and boost growth, currently at 7 percent.
But that move was seen by investors as official endorsement of a slowing economy. A global financial market rout, notably in Chinese stocks, followed and forced the central bank to cut interest rates again, the fifth time since November.
China is a major importer of raw materials, especially from Australia, South Africa and Canada, and exporter of finished goods.
A slowdown there will ring out across the world, denting demand and souring business sentiment. Last week, it figured high on a list of reasons the Fed had for not raising interest rates in the United States for the first time in almost a decade.
Sentiment at Asia's biggest companies tumbled at a record pace in the third quarter on worries about China and the risks it poses to global growth, a Thomson Reuters/INSEAD survey showed.