Global benchmark Brent crude futures rose 67 cents, or 0.8%, to USD 81.51 per barrel by 0007 GMT, while U.S. West Texas Intermediate crude futures rose 69 cents, or 0.9%, to USD 78.60 per barrel.
The most active contracts on both benchmarks jumped about 4% in the previous session.
Hamas leader Ismail Haniyeh was assassinated in the Iranian capital Tehran on Wednesday, less than 24 hours after Lebanon-based Hezbollah's most senior military commander was killed in an Israeli strike in the capital, Beirut.
The killings fuelled concern that the 10-month-old war in Gaza between Israel and Hamas was turning into a wider Middle East war, which could potentially lead to disruptions in oil supply from the region.
"We fear the region is at the brink of all-out war," Japan's deputy United Nations representative Shino Mitsuko said on Wednesday as the U.N. security council called for stepped-up diplomatic efforts.
Also pushing up oil prices was a set of data releases from the U.S., the world's top oil consumer, and a weaker dollar.
Robust export demand pushed U.S. crude oil stockpiles lower by 3.4 million barrels in the week ended July 26 to 433 million barrels, data from the U.S. Energy Information Administration (EIA) showed on Wednesday.
U.S. oil stocks have declined for five consecutive weeks, the longest such streak since January 2021.
U.S. oil demand was at a seasonal record in May as gasoline consumption surged to its highest since before the pandemic, a separate data release from the EIA showed on Wednesday.
Meanwhile, the U.S. dollar index extended losses on Thursday from the previous session, after the Federal Reserve held interest rates steady but left the door open for a cut in September. A weaker dollar can boost oil demand from investors holding other currencies.
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