Brent crude futures were 26 cents, or 0.4%, higher at $74.94 a barrel by 1220 GMT, after slumping 2% on Monday, Reuters reported.
U.S. West Texas Intermediate (WTI) crude futures rose 24 cents, or 0.3%, to $73.15 a barrel, following a 1.5% loss on Monday.
"From a global perspective, there are seemingly growing concerns over the increase in the COVID-19 Delta variant," StoneX analyst Kevin Solomon said.
"The market has grown relatively immune to COVID-19 developments, but if lockdowns occur in larger demand centres in Asia, we may see the market’s nonchalance abate."
Spain and Portugal, favourite summer holiday destinations for Europeans, imposed new restrictions on unvaccinated Britons on Monday, while 80% of Australians faced tighter curbs due to flare-ups of the virus across the country.
However, the market still expects vaccine rollouts to brighten the demand outlook, analysts said.
"The narrative of the past few months has not changed: the war against the virus is being gradually won, the global economy and oil demand are recovering," said PVM Oil analyst Tamas Varga.
"Oil supply is being effectively managed therefore dips are probably viewed by ardent bulls as attractive buying opportunities."
The virus flare-up comes as the Organization of the Petroleum Exporting Countries, Russia and allies, together known as OPEC+, are set to meet on July 1 to discuss easing their supply curbs.
OPEC's demand forecasts show that in the fourth quarter global oil supply will fall short of demand by 2.2 million barrels per day, giving the producers some room to agree to add output.
Analysts expect OPEC+ to step up supply in August as the market has tightened on strong growth in fuel demand in the United States and China, the world's two biggest oil consumers.
Investors will be looking to the latest U.S. inventory data for cues on the outlook for demand. Crude stocks likely extended their fall for a sixth straight week, while gasoline stocks also declined, a preliminary Reuters poll showed.