Brent crude futures climbed 34 cents, or 0.46%, to US$74.84 a barrel at 0508 GMT, extending a 0.5% gain on Monday.
US West Texas Intermediate (WTI) crude futures rose 20 cents, or 0.28%, to $72.11 a barrel, after losing 16 cents on Monday.
Benchmark prices rose even after the United States issued travel warnings to Spain and Portugal due to rising Covid-19 cases and a White House official told Reuters that wider travel curbs will not be lifted due to the highly infectious Delta variant and rising domestic infections.
"Oil prices are set to range this week after recovering all of the "delta-dip" losses from the last Monday week," Jeffrey Halley, a senior Asia Pacific market analyst at OANDA, wrote in a note.
"Both contracts should continue to consolidate their gains, with volatility much reduced from last week."
In one encouraging sign for fuel demand, Britain reported its lowest daily total of new Covid-19 cases since July 4 on Monday, suggesting the recent surge in infections has passed its peak.
Analysts tracking mobility data remain confident about fuel demand, counting on vaccinations to guard against strict new lockdowns.
Global oil markets are expected to remain in deficit despite a decision by the Organization of the Petroleum Exporting Countries (OPEC) and its allies, collectively known as OPEC+, to raise production through the rest of the year.
ANZ Research analysts said "robust road traffic data across most major regions suggests rising infections are having minimal impact".
"Investors are also encouraged by the continued restraint by US shale oil producers. So far they have maintained discipline, with a focus on returns rather than growth," ANZ Research analysts said in a note.
Investors are awaiting inventory data from the American Petroleum Institute industry group on Tuesday and the US Energy Information Administration on Wednesday for further evidence that demand is holding up.
Five analysts polled by Reuters estimated, on average, that US crude stocks fell by about 3.4 million barrels and gasoline stocks fell by 400,000 barrels in the week to July 23. - AFP