Gasoline shortages that have plagued the U.S. East Coast slowly eased on Sunday, with 1,000 more stations receiving supplies as Colonial Pipeline's 5,500-mile (8,900-km) system recovered from a crippling cyberattack.
Brent crude oil futures were up 3 cents at $68.74 a barrel as of 0511 GMT, and West Texas Intermediate (WTI) crude was up 8 cents, or 0.1%, at $65.45.
The two contracts jumped nearly 2.5% on Friday and managed to book a small gain last week, marking a third consecutive weekly increase.
"The market has no clear direction today though a new wave of restrictions to curb the pandemic in Asia is chilling the market mood," said Satoru Yoshida, a commodity analyst with Rakuten Securities.
Investors remained cautious on worries that the highly transmissible coronavirus variant first detected in India is spreading to other countries.
Some Indian states said on Sunday they would extend COVID-19 lockdowns to help contain the pandemic, which has killed more than 270,000 people in the country. There are fears that the nation's annual budget may fall flat as it did not account for a crippling second wave of COVID-19 infections.
Singapore warned on Sunday that new coronavirus variants were affecting more children, as the city-state prepares to shut most schools from this week, while Japan has declared a state of emergency in three more prefectures hit hard by the pandemic.
Disappointing retail data from China also added to pressure, Rakuten's Yoshida said. Chinese retail sales rose 17.7% in April on a year ago, short of forecasts for a jump of 24.8%.
China's crude oil throughput rose 7.5% in April from the same month a year ago, but remained off the peak seen in the last quarter of 2020.
"With growing concerns over the spreading pandemic in Asia, Brent prices are expected to stay in a trading range this week, with support expected at around $63 a barrel," said
Kazuhiko Saito, chief analyst at commodities broker Fujitomi Co.
Meanwhile, U.S. energy firms added oil and natural gas rigs for a third week in a row as higher crude prices prompt some drillers to return to the wellpad, energy services firm Baker Hughes Co said on Friday.
In the Middle East, Israel and Gaza's ruling Hamas militant group faced mounting international calls for a ceasefire in hostilities that entered their second week on Monday with no end in sight.
"As long as the fight does not spill over to oil-producing countries in the region, there will be limited impact on the oil market," Fujitomi's Saito said.
