Brent crude futures fell by 53 cents, or 0.5%, to $96.87 a barrel by 0005 GMT, while U.S. West Texas Intermediate crude futures fell 61 cents, or 0.7%, to $91.32.
U.S. crude oil stocks rose by 5.5 million barrels in the most recent week, the U.S. Energy Information Administration said, more than the expected increase of 73,000 barrels.
Gasoline product supplied rose in the most recent week to 9.1 million barrels per day, though that figure still shows demand down 6% over the past four weeks compared with the year-ago period.
Flows on the Russia-to-Europe Druzhba pipeline resumed earlier this week.
Russian state oil pipeline monopoly Transneft restarted oil flows via the southern leg of the Druzhba oil pipeline. Ukraine had suspended Russian oil pipeline flows to parts of central Europe since early this month because Western sanctions prevented it from receiving transit fees from Moscow, Transneft said on Tuesday.