* European refinery-run cuts reducing physical demand
* U.S., China data fuels hope economy is stabilizing
* Coming up: EIA weekly oil data at 10:30 a.m. EDT Wednesday (Updates U.S. trading range, adds API data, paragraphs 3, 13-15)
By Robert Gibbons
NEW YORK, June 3 (Reuters) - Brent crude steadied and U.S. crude erased earlier losses to push higher on Tuesday as economic data from the United States and China supported prices that have been under pressure recently because of increasing global oil production.
Brent July crude fell 1 cent to settle at $108.82 a barrel. Brent ended above its 50-day moving average of $108.56 after sliding earlier to $108.32, two cents above its 100-day moving average.
U.S. July crude rose 19 cents to settle at $102.66, reaching $102.86 at 5 p.m. EDT (2100 GMT)in post-settlement trading.
"I think technically Brent has broken to the downside and that it will trend lower gradually," said Christopher Bellew, an oil broker at Jefferies Bache in London. "However, the market is pretty well-balanced fundamentally and geopolitical risk is still with us, so I do not envisage prices going below $105."
Recent weakness in Europe's physical oil market, where differentials narrowed to two-year lows last week, has weighed on Brent prices even as turmoil in Ukraine and supply disruption in Libya fuel the geopolitical risk premium for oil.
European oil refiners are cutting operating rates by nearly one quarter ahead of the peak summer period.
New orders for U.S. factory goods rose for a third straight month in April and data released earlier on Tuesday pointed to China's factory sector having its best performance in four months during May.
"The market received a little bit of a boost from those Chinese numbers - it paints a picture of continued slow recovery and stabilization," said Ole Hansen, senior commodity strategist at Saxo Bank. "This should support oil demand growth in China."
Ukraine's crisis with Russia, one of the world's top oil producers, is still a concern, along with turmoil in Libya, where the eastern port of Hariga remained closed by protesting security guards.
"The market is chopping around and everybody's waiting on the storage data and cautious before the OPEC meeting," said Robert Yawger, director for energy futures at Mizuho Securities USA, referring to the Organization of the Petroleum Exporting Countries' meeting in Vienna on June 11.
U.S. crude stocks were expected to be off by 300,000 barrels last week, according to a Reuters analyst survey.
Along with booming U.S. crude oil production, crude prices have been curbed by rising production from OPEC, with Iraq output up 8 percent in May.
Oil futures had a muted reaction to American Petroleum Institute data released late on Tuesday showing U.S. crude stocks fell 1.4 million barrels last week, with stocks at the Cushing, Oklahoma, hub falling 300,000 barrels.
Gasoline inventories rose 800,000 barrels and distillate stocks fell 300,000 barrels, the API said.
The U.S. Energy Information Administration's data is due on Wednesday at 10:30 a.m. EDT. (Additional reporting by Claire Milhench in London and Florence Tan in Singapore, Editing by David Evans, Susan Thomas, Marguerita Choy and Peter Galloway)