LONDON, June 27 Reuters Oil prices were largely steady on Thursday as a surprise build in U.S. stockpiles fuelled fears about slow demand from the world39;s top oil consumer and countered supply concerns stoked by escalating conflict in the Middle East.

Brent crude oil futures were up 43 cents, or 0.5, at 85.68 a barrel by 0850 GMT. U.S. West Texas Intermediate crude futures rose 42 cents, or 0.5, to 81.32.

Both benchmarks had settled slightly higher on Wednesday.

The U.S. Energy Information Administration EIA reported a 3.6 million barrel jump in the country39;s crude oil stocks last week. Analysts polled by Reuters had expected a drawdown of 2.9 million barrels.

U.S. gasoline stocks also rose, increasing by 2.7 million barrels. That compared with analyst expectations for a 1 million barrel draw.

The actual readings were nothing short of disappointing for bulls that look for a continued market tightening brought about by seasonal demand, said PVM Oil analyst John Evans.

If it were not for the steady and incremental ratcheting up of geopolitical risk in the Middle East, oil prices might have found themselves on the back end of a much more negative day.

Worries over the potential for the the IsraelHamas war in Gaza spreading to Lebanon limited price declines.

Crossborder strains between Israel and Lebanon39;s Hezbollah have been escalating in recent weeks, stoking fears of a war that could draw in other regional powers, including major oil producer Iran.

Turkish…