* U.S. crude stocks rise, gasoline inventories fall
* Conflict in Europe, Middle East support oil prices
SINGAPORE, June 19 (Reuters) - Oil prices held steady during trade on Wednesday, as the market weighed concerns over escalating conflict in Europe and the Middle East with demand worries following an unexpected build in U.S. crude inventories.
Brent crude futures rose 2 cents to $85.35 a barrel by 0350 GMT, while U.S. West Texas Intermediate crude was down 6 cents to $81.51 per barrel.
Both benchmarks gained over $1 in the previous session after a Ukrainian drone strike led to an oil terminal fire at a major Russian port, according to Russian officials and a Ukrainian intelligence source.
In the Middle East, Israeli Foreign Minister Israel Katz warned of a nearing "all out war" with Lebanon's Hezbollah, even as the U.S. attempted to avoid a broader conflict between Israel and Iran-backed Hezbollah.
An escalating war in the region raises the prospect crude supply from key producers could be disrupted.
"Market participants are back to price for potential disruption risks in the event of a wider conflict as geopolitical tensions are brought to a new front between Israel and Hezbollah," said Yeap Jun Rong, a market strategist at IG in Singapore.
"Any cooling off between both parties seems difficult in the near term, which may keep oil prices well-supported as market participants shrug off pockets of weakness on the economic front, from weaker-than-expected U.S. retail sales to mixed sets of data out of China this week."
China data this week showed May industrial output lagged expectations, but retail sales as a gauge of consumption marked its quickest growth since February.
Analysts in a ANZ Research report on Wednesday said a broader risk-on tone across global markets supported crude oil prices, with mixed U.S. economic data for May boosting bets that the Federal Reserve will cut rates sooner rather than later, referring to strong industrial production and retail sales that barely rose.
Federal Reserve officials are looking for further confirmation that inflation is cooling and for any warning signs from a still-strong labor market, as they steer cautiously toward what most expect to be an interest rate cut or two by the end of this year.
Interest rate cuts could reduce borrowing costs, spurring economic activity and lifting oil consumption.
Keeping oil prices from rising further however, U.S. crude stocks rose by 2.264 million barrels in the week ended June 14, according to market sources citing American Petroleum Institute figures on Tuesday. Analysts polled by Reuters had expected a 2.2 million barrel draw in crude stocks.
Gasoline inventories, however, fell by 1.077 million barrels, while distillates rose by 538,000 barrels, the sources said, speaking on condition of anonymity.
Official U.S. stocks data from the Energy Information Administration are due at 1500 GMT.
(Reporting by Laila Kearney in New York and Emily Chow in Singapore; Editing by Sonali Paul and Miral Fahmy)
