Brent crude futures LCOc1 rose $0.59, or 1.4%, to $43.81 a barrel by 1216 GMT.
US inventories fell by 10.6 million barrels last week, compared with analyst expectations for a gain, Energy Information Administration data showed.
Prices were anchored on Thursday by demand concerns with a rise in COVID-19 infections raising the prospect for lockdowns to be reimposed.
US West Texas Intermediate (WTI) crude futures were down 70 cents, or 1.7 per cent, at $40.57 a barrel.
Oil prices sank on Thursday following poor U.S. economic figures and after U.S. President Donald Trump roiled markets with a suggestion that the nation should delay its November presidential election.
Meanwhile, shipping data shows Iraq's crude oil exports have increased so far in July by 50,000 barrels per day (bpd), suggesting that it is not adhering to its OPEC production target - but that the rise may be another indication of market recovery nonetheless.
"Despite the resilient and range-bound nature of oil pricing over recent weeks, plateauing global demand and increasing OPEC+ output raises the question of whether the market can absorb additional barrels", RBC Capital Markets said in a note.
"The expectation is that the OPEC cuts are going to lead to bigger draws in the United States and this could be the beginning of it", said Phil Flynn, senior analyst at Price Futures Group in Chicago.
The dollar extended its dramatic fall on Friday and was on course for its biggest monthly drop in a decade after news on Thursday that USA gross domestic product collapsed at a 32.9% annualized rate - the steepest decline in output since records began in 1947.
Deaths from COVID-19 have now topped 150,000 in the United States, while Brazil, with the world's second-worst outbreak, set daily records of confirmed cases and deaths.
Attempts to provide relief amid the outbreak were in disarray as Republicans in the U.S. disagreed over their own plan for providing $1 trillion in new coronavirus aid on Tuesday.
Oil prices rose on Friday and were on track for monthly gains, boosted by a weaker dollar in the face of continuing concerns over the recovery of the US economy as the coronavirus ravages the world's biggest economy and oil consumer.