(Reuters) -Oil prices ticked up on Thursday as optimism built that potential U.S. interest rate cuts will boost economic activity and fuel consumption, but concerns over slower global demand curbed gains.

Brent crude futures were up 51 cents, or 0.6%, at $80.27 a barrel at 1107 GMT, recovering some of the previous day's losses. U.S. West Texas Intermediate crude futures were up 47 cents, or 0.6%, at $77.45 per barrel.

Both benchmarks fell more than 1% on Wednesday after U.S. crude inventories rose unexpectedly.

U.S. consumer prices rose moderately in July and the annual increase in inflation slowed to below 3% for the first time in nearly 3-1/2 years, reinforcing expectations the Federal Reserve will cut interest rates next month.

"Crude oil prices inched higher during the early European session due to increased risks of a flare-up in confrontations in the Middle East," said Milad Azar, market analyst at brokerage XTB.

"Optimism that potential U.S. interest rate cuts could spur economic growth and increase fuel consumption has also supported oil prices."

Investor worries over Iran's potential response to the killing of the leader of the Palestinian militant group Hamas last month supported prices. Three senior Iranian officials have said that only a ceasefire deal in Gaza would hold Iran back from direct retaliation against Israel for the assassination.

"Geopolitical risk continues to hang over the oil market. It is still unclear how and if Iran will retaliate against Israel," ING analysts said in a client note.

However, oil inventory gains raised concerns of weaker demand, analysts at ANZ said in a client note. U.S. crude oil stockpiles rose by 1.4 million barrels in the week ended Aug. 9, compared with estimates for a 2.2 million barrel draw, building for the first time since late June. [EIA/S]

China's factory output growth slowed in July while refinery output fell for a fourth month, underscoring the country's spotty economic recovery, also limiting the market's upside.

(Additional reporting by Yuka Obayashi in Tokyo and Trixie Yap in Singapore; Editing by David Evans and Mark Potter)