U.S. crude was at $39.93 a barrel, up 39 cents, or 1.01%.
Brent crude rose 26 cents, or 0.62%, to $42.16 a barrel.
Both contracts rose about 9% last week and Brent crude futures have flipped into backwardation, where oil for immediate delivery costs more than supply later, usually an indication of tightening supply.
“The market has entered a slight backwardation up to October. It times in with some of our estimates that by around November, the market could get really tight, said Howie Lee, an economist at Singapore’s OCBC bank.
“I find it more difficult for oil to move higher at this point in time, especially with the growing concern about second-wave contagion,” Lee said.
In the United States and Canada, the number of operating oil and natural gas rigs fell to a record low last week even as higher oil prices prompt some producers to start drilling again.
The OPEC+ group, consisting of Organization of the Petroleum Exporting Countries and its allies including Russia, has yet to decide whether to extend a record supply cut of 9.7 million barrels per day (bpd) for a fourth month in August.
However, Iraq and Kazakhstan pledged to comply better with oil production cuts during an OPEC+ panel on Thursday.
Oil prices have also been supported by a recovery in fuel demand globally following a collapse in April-May during coronavirus shutdowns as countries across the world resume economic activities.
Still, the World Health Organization reported a record jump in global coronavirus cases on Sunday, with the biggest increase seen in north and south America.
“The potential economic damage of a new round of COVID-19 countermeasures will likely contain any investor enthusiasm,” said Michael McCarthy, chief market strategist at CMC Markets.
Spikes in coronavirus infections in parts of the world such as Beijing and Australia’s second-most populous state Victoria have prompted authorities to reimpose movement restrictions to curb the spread.