Brent crude futures rose 60 cents, or 0.7%, to $86.87 a barrel at 0528 GMT, reversing a 1.8% fall in the previous session.
U.S. West Texas Intermediate (WTI) crude futures climbed 45 cents, or 0.5%, to $83.76 a barrel, having slid 2.2% on Monday.
Oil prices reached seven-year highs last week, bolstered by tight worldwide supply and resurgent global demand.
"The market tone stays strong, supported by heightening geopolitical risk," said Chiyoki Chen, chief analyst at Sunward Trading.
OPEC+, which groups the Organization of the Petroleum Exporting Countries (OPEC) with Russia and other producers, is struggling to hit its monthly output increase target of 400,000 barrels per day (bpd).
Lower U.S. oil inventories are also providing support, with crude inventories around the NYMEX WTI delivery point at Cushing in Oklahoma at the lowest for the time of year since 2012.
Portfolio investors added to their bullish positions in oil for the fifth week running, as the worst of the latest wave of coronavirus infections passed and governments began to lift restrictions on business and travel.