By Noah Browning

LONDON (Reuters) -Oil prices edged higher on Thursday as supply disruption risks from rising geopolitical tensions in the Middle East helped to counter demand fears after a surprise build in U.S. stockpiles.

futures gained 70 cents, or 0.82%, to $85.95 a barrel by 1202 GMT. U.S. West Texas Intermediate crude futures rose 57 cents, or 0.7%, to $81.47.

Both benchmarks had settled slightly higher on Wednesday.

The U.S. Energy Information Administration (EIA) reported a 3.6 million barrel jump in the country’s stocks last week. Analysts polled by Reuters had expected a drawdown of 2.9 million barrels. [EIA/S]

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 Israel-Hamas war in Gaza spreading to Lebanon limited price gains.

Cross-border strains between Israel and Lebanon’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.

Were contagion to occur, it could have a significant impact on crude supplies from the Middle East, said Panmure Gordon analyst Ashley Kelty.

Turkish President Tayyip Erdogan said his country stood in solidarity with Lebanon and called on the region’s countries to show their support.

Israeli forces pounded several areas across Gaza on Wednesday and residents reported fierce fighting overnight in Rafah in the south of the Palestinian enclave.