New York's main contract, light sweet crude for delivery in March, increased three cents to $97.97 a barrel and Brent North Sea crude for March delivery gained 27 cents to $115.17.
"Some geopolitical risk premium has crept into oil futures," said Victor Shum, managing director at IHS Purvin and Gertz in Singapore, referring to the attack.
The Syrian army accused Israel of launching a dawn strike targeting a military research centre in Jamraya, near Damascus on Wednesday, in a statement carried by state news agency SANA.
Analysts said the attack increased the risk that the 22-month-old conflict in Syria could spill over into neighbouring states, sparking fears of supply disruption in the Middle East, the world's biggest crude supplier.
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Other analysts said global energy demand remained relatively weak with robust supplies.
"Crude oil market fundamentals are still thought to be fairly weak, with some building pressures on OPEC (Organisation of the Petroleum Exporting Countries) to rein in production," said Sanjeev Gupta, who heads the Asia Pacific oil and gas practice at Ernst & Young.
He said markets were waiting for the release of fourth-quarter economic growth figures in the United States and "any bearish economic signals... could push prices into a modest retreat".