Brent crude futures were down 30 cents, or 0.4%, at $68.16 a barrel by 1004 GMT, having jumped 3% on Monday. US West Texas Intermediate futures were off 42 cents, or 0.6%, at $65.63 a barrel, after gaining 3.9% the previous session.
Still, the global recovery from the COVID-19 pandemic is patchy, indicating a mixed outlook for oil demand.
Chevron, the second-largest US oil producer, reported a profit of $1.72 billion, or 90 cents per share, compared with $2.45 billion, or $1.31 per share, a year earlier. Year-ago results included about $680 million in asset sales and favorable tax items.
Net profit was $1.4 billion, or 72 cents a share, down from $3.6 billion, or $1.93 cents a share, a year earlier.
Brent crude futures for June fell 32 cents, or 0.32%, to $62.88 a barrel.
Both contracts are on track for a 2%-3% drop this week but still far from a low of $60.47 hit two weeks ago. Exerting downward pressure is the decision by the Organization of the Petroleum Exporting Countries (OPEC) and its allies, known as OPEC+, to increase supplies by 2 million barrels per day between May and July.