Brent crude oil futures rose 12 cents, or 0.2%, to $57.83 a barrel by 0703 GMT, while U.S. West Texas Intermediate (WTI) crude futures rose 9 cents, or 0.2%, to $52.54.
"Today in Asia I believe we are seeing some pre-weekend buying, mostly as a risk hedge against anything happening in the Middle East over the weekend," said Jeffrey Halley, a senior market analyst at OANDA in Singapore.
Still, for the week, Brent was down 6.6%, marking its largest weekly loss since December. WTI was down 6% for the week, its biggest decline since July.
"The supply side of the equation will continue to weigh on oil as full Saudi Arabia production returns much faster than expected," Halley said.
Weak U.S. services sector and jobs growth data on Thursday added to worries about global oil demand and exacerbated fears that a protracted U.S.-China trade war could push the global economy into a recession.
"Concerns about global oil demand are rising, and next week's U.S.-China trade talks, the significant X factor, will be particularly important, given the sharp drop in the oil price over the last week," said Stephen Innes, Asia Pacific market strategist at AxiTrader.
Saudi Arabia's energy minister, Prince Abdulaziz bin Salman, also said on Thursday the world's top crude oil exporter has fully restored oil output after attacks on its facilities last month knocked out more than 5% of global oil supply.
Recent data showing a slowdown in U.S. shale output and drilling activity, however, could lend some support.
"Continued falls in drilling activity has seen monthly growth in U.S. shale oil output fall, from 150 thousand barrels per day (kbpd) to only 50 kbpd," said ANZ Bank on Friday.
"This is likely to linger well into 2020."