Brent crude was up 14 cents, or 0.3%, at $45.10 by 0043 GMT, heading for a gain of about 1.6% this week.
West Texas Intermediate had gained 12 cents, or 0.3%, to $42.36. The U.S. benchmark is heading for a gain of nearly 3% this week.
“The situation has improved some, but the market dynamics are still less than stellar,” said Robert Yawger, director of energy futures at Mizuho Securities, adding “the market is oversupplied”.
Prices have been bolstered this week by U.S. government data showing crude oil, gasoline and distillate inventories all fell last week as refiners ramped up production and demand for oil products improved.
Still, the International Energy Agency has reduced its oil demand forecast for this year, and said lower air travel due to the COVID-19 pandemic would cut global oil consumption this year by 8.1 million barrels per day (bpd).
The Organization of the Petroleum Exporting Countries (OPEC) said earlier this week that world oil demand is likely to drop by 9.06 million bpd this year, a bigger decline than the 8.95 million bpd decline expected a month ago.
OPEC and allies including Russia, collectively called OPEC+, cut output since May by around 10% of typical global demand to tackle the fallout from the global health crisis.
Meanwhile, Russian Energy Minister Alexander Novak said he does not expect quick decisions on output cuts when an OPEC+ group monitoring committee meets next week, Russian news agencies reported on Thursday.