(Corrects Brent price in headline and paragraph 1)
* Euro zone manufacturing shrinks, outlook dims
* U.S. crude, products stocks rose last week-API
* Coming up: EIA oil data at 1430 GMT
By Jessica Jaganathan
SINGAPORE, July 25 (Reuters) - Brent slipped below $103 a barrel on Wednesday as worries about oil demand from the troubled euro zone offset any gains to prices sparked by concerns about oil supply from the Middle East.
The euro zone's private sector shrank for a sixth month in July as manufacturing output nosedived, notably in the core countries of Germany and France, adding to the likelihood that the bloc will slump back into recession, business surveys showed on Tuesday.
Also weighing on prices was further evidence that the economy of the world's biggest oil consumer was slowing: data showed U.S. manufacturing activity in July expanded at its slowest pace since late 2010.
Brent crude slipped 55 cents to $102.87 a barrel by 0651 GMT while U.S. crude fell 66 cents to $87.84.
"After the sharp drop on Monday, Brent has been trading within a narrow range as there are still some concerns on the euro zone economy, so there's some room for it to decline," said Ken Hasegawa, a commodity sales manager at Newedge Japan.
"The Chinese PMI data had a small impact but there is still a lot of uncertainty on the euro situation ... Brent will probably stay in the range of $98-$108 over the next few months."
Spain on Tuesday paid the second-highest yield on short-term debt since the euro's birth, which investors interpreted as another sign the country will likely need a full sovereign bailout.
An improvement in China's manufacturing sector in July propped up prices on Tuesday but reports that the economy of the world's second biggest oil consumer was still weakening added to the bearish mood.
The International Monetary Fund said China's economy is set for a soft landing and urged further reform and currency appreciation to rebalance growth and reduce risks.
China's Ministry of Industry and Information Technology said economic growth will likely pick up in the second half of 2012 as a raft of policies rolled out to boost economic activity gain traction, but warned that the economy still faces severe challenges at home and abroad.
Also affected by the global slowdown, Japan's exports fell in June from a year earlier, the first decline in four months.
An unexpected rise in U.S. crude oil stocks also kept prices lower. U.S. crude stocks rose 1.3 million barrels last week, the industry group American Petroleum Institute said in its weekly report on Tuesday, surprising analysts who expected a decline.
U.S. crude oil inventories had been forecast to drop 700,000 barrels, with distillate stocks having risen 1.1 million barrels and gasoline stocks slipping 600,000 barrels, a Reuters poll taken ahead of weekly inventory reports showed.
Despite the notable slowdown in global economic growth, Goldman Sachs analysts expect oil demand to grow well in excess of production capacity growth.
"In our view, it is only a matter of time before inventories and OPEC spare capacity become effectively exhausted, requiring higher oil prices to restrain demand, keeping it in line with available supply," they said in a note on Tuesday.
Supporting prices was the escalating violence in Syria, as well as the tensions between Iran and the West over Tehran's nuclear programme.
Syria sent thousands of troops towards Aleppo in the early hours of Wednesday, where its forces have been pounding rebel fighters from the air, engulfing the country's largest city in total warfare to put down a revolt.
The oil market is precariously balanced between a deteriorating macro situation and near term supply-side risk, analysts from National Australia Bank said in a note on Wednesday.
"This tug of war between competing influences on crude oil prices is likely to remain through the second half of 2012," they said. "With sanctions beginning to bite, Iran is likely to become increasingly desperate geo-politically thereby maintaining the risk premium that has been built in." (Editing by Miral Fahmy and Alison Birrane)