Front-month Brent crude oil futures LCOc1 were at $71.89 per barrel at 0621 GMT, down 18 cents, or 0.3 percent from their last close.
U.S. West Texas Intermediate (WTI) crude futures CLc1 were down by 25 cents, or 0.4 percent, at $66.56 a barrel.
Prices eased on a possible slowdown in economic growth due to escalating trade tensions.
For the week, Brent is set for a near 2 percent fall, while WTI is heading for a drop of nearly 3 percent.
“The market seems to be focused on fears of reduced demand from China, partially due to the effects of the trade wars between China and the United States,” said William O’Loughlin, investment analyst at Australia’s Rivkin Securities.
In the latest round of tariffs, China said it would impose additional tariffs of 25 percent on $16 billion worth of U.S. imports.
Although crude was removed from the list, replaced by refined products and also liquefied petroleum gas (LPG), many analysts say Chinese imports of American crude will still fall significantly.
“Already we are hearing that Chinese refiners are holding back on U.S. crude, despite escaping tariffs,” ANZ bank said.
Growing global trade tensions have also led to a slump in the currencies of major emerging economies such as India, Turkey and China.
These devaluations have made imports of oil, which is traded in U.S. dollars, more expensive, potentially denting demand.
“The major devaluation of many emerging market currencies relative to the U.S. dollar means that in local terms oil is higher than what we see on the screen,” U.S. investment bank Jefferies said on Friday.
While the demand outlook was getting gloomier, supplies may tighten with the re-introduction of U.S. sanctions against Iran, which from November will also include oil exports.
Although other powers, including the European Union, China and India oppose sanctions, many are expected to bow to American pressure.
“We do not believe that sanctions have been fully priced into Brent, leaving room for a significant run-up in prices towards the end of the year,” BMI Research said.
Analysts expect the drop-off in Iranian crude exports to range between 500,000 barrels per day (bpd) and 1.3 million bpd, with buyers in Japan, South Korea and India already dialing back orders.
The reduction will depend on whether major buyers of Iranian oil in Asia receive sanctions waivers that would still allow some imports.
It was also not clear whether China, the biggest buyer of Iranian crude, will bow to Washington’s pressure.