Brent crude futures rose 17 cents, or 0.2%, to $79.40 a barrel at 0217 GMT, climbing for a fourth day in a row.
U.S. West Texas Intermediate (WTI) crude futures rose 23 cents, or 0.3%, to $76.79 a barrel for a seventh straight session of gains.
U.S. Energy Information Administration data on Wednesday showed crude oil inventories fell by 3.6 million barrels in the week to Dec. 24, which was more than analysts polled by Reuters had expected.
At the same time gasoline and distillate inventories fell, compared with analysts' forecasts for stock builds, indicating demand remains strong.
Further supporting sentiment, governments around the world were trying to limit the impact of record numbers of new COVID-19 infections on economic growth by easing testing rules and narrowing who needs to isolate as close contacts of positive cases.
China, the world's biggest oil importer, reported 207 new confirmed coronavirus cases and 27 new asymptomatic cases on Thursday, but no new deaths. Australian cases hit a new record of more than 19,000 daily infections.
