Brent crude was up 82 cents, or 1.3 percent, at $62 a barrel at 1200 GMT. Brent has risen more than 2 percent this week, its third straight week of gains, Reuters reported.
U.S. West Texas Intermediate (WTI) crude futures were up 78 cents, or 1.5 percent, at $52.85 per barrel.
The Organization of the Petroleum Exporting Countries along with other producers including Russia agreed last year to output cuts starting from Jan. 1 aimed at averting a glut.
OPEC's monthly report showed it had made a strong start in December even before the pact went into effect, implementing the biggest month-on-month production drop in almost two years.
Expectations that the United States may grant waivers on sanctions it imposed on importing Iranian oil to fewer countries could also ease concerns about oversupply.
"The combination of production cuts by OPEC+ (especially the Saudis) and tightening sanctions on Iranian oil exports have brought the market close to balance," US investment bank Jefferies said.
Tempering support for prices, however, are signs of weakening demand and surging US output.
"Implementation of the output cut agreement agreed by the OPEC+ will remain supportive of oil prices," said Abhishek Kumar, senior energy analyst at Interfax Energy in London.
He said factors such as rising US production and its trade dispute with China would cap price gains, "negating much of the benefits from the OPEC+ pact".
The International Energy Agency said on Friday that US oil production growth combined with a slowing global economy would put oil prices under pressure.
"By the middle of the year, US crude output will probably be more than the capacity of either Saudi Arabia or Russia," said the IEA, which kept its estimate of oil demand growth unchanged and close to 2018 levels at 1.4 million barrels bpd.
Markets were also buoyed by signs that the United States and China might soon resolve their trade dispute in talks scheduled for Jan. 30.
The Wall Street Journal reported on Thursday that Washington was considering lifting some or all tariffs imposed on Chinese imports. A Treasury spokesperson denied the report.