Brent crude futures were down 19 cents, or 0.3 percent, at $67.90 a barrel by 1210 GMT and US West Texas Intermediate (WTI) crude fell by 21 cents, or 0.3 percent, to $64.50, Reuters reported.
Both Brent and WTI are on track for second consecutive weekly gains as easing restrictions on movement in the United States and Europe, recovering factory operations and coronavirus vaccinations pave the way for a revival in fuel demand.
In China, data showed export growth accelerated unexpectedly in April while a private survey pointed to strong expansion in service sector activity.
However, crude imports by the world's biggest buyer fell 0.2 percent in April from a year earlier to 40.36 million tons, or 9.82 million barrels per day (mbd), the lowest since December.
In the United States, the world's largest oil consumer, jobless claims have dropped, signaling the labor market recovery has entered a new phase as the economy recovers.
The recovery in oil demand, however, has been uneven as surging COVID-19 cases in India reduce fuel consumption in the world's third-largest oil importer and consumer.
"Brent came within a whisker of breaking past $70 a barrel this week but failed at the final hurdle as demand uncertainty dragged on prices," said Stephen Brennock at oil brokerage PVM.
The resurgence of COVID-19 in countries such as India, Japan and Thailand is hindering gasoline demand recovery, energy consultancy FGE said in a client note, though some of the lost demand has been offset by countries such as China, where recent Labor Day holiday travel surpassed 2019 levels.
"Gasoline demand in the US and parts of Europe is faring relatively well," FGE said.
"Further out, we could see demand pick up as lockdowns are eased and pent-up demand is released during the summer driving season."