Brent crude gained 25 cents, 0.4%, to $65.65 a barrel at 11:46 a.m. EDT (1536 GMT), while U.S. West Texas Intermediate (WTI) U.S. crude gained 20 cents, or 0.3%, to $61.63 a barrel.
Both benchmark crudes were headed for a weekly loss of more than 2% due to the resurgence of infections in India and Japan, respectively the world's third and fourth largest oil importers.
"This price consolidation follows a strong four-month price advance that was largely predicated on U.S. vaccine progress that forced some upward revisions in global demand ideas across this year," said Jim Ritterbusch, president of Ritterbusch and Associates in Galena, Illinois.
Euro zone Purchasing Managers' Index (PMI) data for April showed a stronger than expected recovery and more European states began easing coronavirus lockdowns. France said schools would reopen on Monday.
"Stronger PMIs across Europe, a weaker U.S. dollar, and some European countries planning to ease some of their restrictions are slightly supporting oil prices," UBS oil analyst Giovanni Staunovo said.
Adding to the more upbeat outlook in European and U.S. economic data, the number of Americans filing new claims for unemployment benefits fell to a 13-month low last week.
U.S. refiner Valero said demand for gasoline and diesel were at 93% and 100% of pre-pandemic levels.
International oil activity should ramp up through the end of this year and beyond, Schlumberger NV top boss Olivier Le Peuch said.
U.S. drilling has been on the rise since the rig count hit a record low in August. This week's drilling data from Baker Hughes is due at 1 p.m.
However, demand concerns weigh on the oil market as coronavirus cases surge to record highs in India.
Several countries, including Australia, Britain, Canada, and the United Arab Emirates have barred or cut flights from India.
Japan declared new lockdowns in Tokyo, Osaka and two other prefectures on Friday.
(Additional reporting by Bozorgmehr Sharafedin in London, additional reporting by Sonali Paul in Melbourne and Koustav Samanta in Singapore; Editing by Marguerita Choy and Edmund Blair)
By Laura Sanicola