U.S. West Texas Intermediate (WTI) crude futures rose 27 cents, or 0.4%, to $66.77 a barrel at 0122 GMT, adding to a 1.4% gain on Thursday.
Brent crude futures rose 12 cents, or 0.2%, to $69.79 a barrel, after climbing 1.2% in the previous session.
The Organization of the Petroleum Exporting Countries, Russia and allies, together called OPEC+, surprised the market on Thursday when it stuck to plans to add 400,000 barrels per day (bpd) supply in January.