Brent was up 25 cents, or 0.4 per cent, at $63.20 a barrel by 0155 GMT. U.S. crude gained 17 cents, or 0.3 per cent, to $59.49 a barrel.
Prices have changed little since a period of volatile trading ended with the close of trading last Monday.
“An unsettling calm has enveloped oil markets recently as Brent remains anchored around $63 and traders adopt a wait=and-see range-trade mentality,” said Stephen Innes, chief market strategist at Axi.
While the United States has fully vaccinated more than 70 million people, and in Europe new infection numbers are falling as lockdowns take effect, India is reporting record new cases and other parts of Asia are seeing caseloads rise.
That is likely to continue to “sully the global travel outlook” and keep prices rangebound as the summer approaches, Innes said.
The U.S. economy is at an “inflection point” amid expectations that growth and hiring will accelerate in the months ahead, but faces the risk of reopening too quickly and sparking a resurgence in coronavirus cases, Federal Reserve Chair Jerome Powell said in an interview broadcast on Sunday.
“There really are risks out there. And the principal one just is that we will reopen too quickly, people will too quickly return to their old practices, and we’ll see another spike in cases,” Powell said in a CBS interview, recorded on Wednesday.