By Nicole Jao

NEW YORK (Reuters) - Oil prices fell to two-month lows on Wednesday as a surprise build in U.S. fuel stockpiles signalled demand weakness and a potential peace deal between Russia and Ukraine continued to weigh on prices.

Brent crude settled down 49 cents, or 0.67%, at $72.53 a barrel. U.S. West Texas Intermediate crude oil futures fell by 31 cents, or 0.45%, to $68.62.

Both benchmarks settled at their lowest since December 10.

U.S. gasoline and distillate inventories posted surprise builds last week even though crude oil stockpiles fell unexpectedly as refining activity ticked higher, the Energy Information Administration said.

"We had a knee jerk reaction down to the low. It was a bit of a surprise because of the crude oil number was a pretty big draw," said Bob Yawger, director of energy futures at Mizuho.

Prospects for a peace deal between Russia and Ukraine are improving, ING commodities strategists said in a note, adding the market was also watching for implications of a minerals deal between the U.S. and Ukraine.

"This would take us a step closer to Russian sanctions being lifted, removing much of the supply uncertainty hanging over the market," the note said.

Downside risks on oil prices increased because of U.S. President Donald Trump's policies, such as initiatives to support higher oil exports by Iraq, said Saxo Bank analyst Ole Hansen. Trump's tariff policies could also trigger a trade war and curb economic growth, Hansen added.

The U.S. and Ukraine agreed on terms of a draft minerals deal central to Trump's efforts to bring a swift end to the war in Ukraine, sources familiar with the matter told Reuters on Tuesday.

Fears that a trade war could slow demand have eased worries about tighter near-term oil supply despite fresh U.S. sanctions against Iran, ANZ Bank analysts said in a note.

Trump announced a reversal of concessions given to Venezuela by former President Joe Biden in 2022.

The Biden administration allowed Chevron to expand its production in Venezuela and bring the country's crude oil to the U.S.

(Reporting by Nicole Jao and Shariq Khan in New York, Enes Tunagur in London and Jeslyn Lerh in Singapore; Editing by David Goodman, Rod Nickel and David Gregorio)