Brent crude was down 8 cents, or 0.2%, at $39.98 a barrel by 0110 GMT, after falling nearly 2% on Thursday, while U.S. crude was off by 2 cents at $37.28 a barrel, having fallen 2% in the previous session.
Both major benchmarks were headed for a second week of declines.
In the United States, stockpiles rose last week against expectation as refineries slowly returned to operations after production sites were shut down due to storms in the Gulf of Mexico and wider region.
"Crude production is starting to return following a couple of storms, but a weak demand outlook and the start of maintenance season will keep the pressure on oil prices," said Edward Moya, senior market analyst at OANDA.
Crude inventories in the United States rose 2.0 million barrels last week, against expectations for a 1.3 million-barrel decrease in a Reuters poll.
In a further bearish sign, traders were starting to book tankers again to store crude oil and diesel, amid a stalled economic recovery as the COVID-19 pandemic continues unabated.
Onshore storage remains near capacity as supplies continue to outpace demand, so the use of so-called floating storage is back in vogue as cheap financing costs and the spread between contracts for delivery now and later months makes it favourable for traders to hold oil for later sale.
(Reporting by Aaron Sheldrick; editing by Richard Pullin)
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