Crude was still heading for its first weekly drop in five weeks, pressured by a big rise in US inventories and fading concerns for now that looming US sanctions on Iran will cut supplies significantly.
Oil found support on Friday from a gain in world stocks. A drop in equities amid wider risk-off investor sentiment had pressured crude on Thursday.
"A rebound in equity markets would help Brent to rebound from $80," said Olivier Jakob, analyst at Petromatrix, adding that a dip below $80 on Thursday did not clearly break that level as a source of technical support.
International benchmark Brent crude rose 34 cents to $80.60 a barrel by 1052 GMT, having dropped by 3.4 percent on Thursday. US crude added 45 cents to $71.42.
Still, the monthly report by the International Energy Agency (IEA) on Friday weighed. The IEA said the market looked "adequately supplied for now" and trimmed its forecasts for world oil demand growth this year and next.
"This is due to a weaker economic outlook, trade concerns, higher oil prices and a revision to Chinese data," said the IEA, which advises industrialised countries on energy policy.
The IEA report is the latest government assessment to predict weaker demand ahead and conclude that supply is adequate. The Organization of the Petroleum Exporting Countries (OPEC) made a similar move on Thursday.
"The bearish alarm bells are ringing for next year's oil balance as market players brace for the return of a supply surplus," said Stephen Brennock of oil broker PVM.
A drop in US oil production also lent prices some support. In the US Gulf of Mexico, companies cut output by 40 percent on Thursday because of Hurricane Michael, even as some operators began returning crews to offshore platforms.
Michael made landfall in Florida on Wednesday as the third most powerful hurricane to strike the US mainland, though it has since weakened to a tropical storm.