Brent crude futures were down 28 cents, or 0.40%, to $68.93 a barrel.
US West Texas Intermediate (WTI) crude was at $66.83 a barrel, down 37 cents, or 0.55%. Both benchmarks settled slightly lower on Monday.
The August WTI contract expires on Tuesday and the more active September contract was down 29 cents, or 0.44%, to $65.66 a barrel.
"Broad demand concerns continue to simmer amid escalating global trade tensions, especially as markets eye the latest tariff threats between major economies and Trump's potential announcements ahead of the August 1 deadline," said Priyanka Sachdeva, Senior Market analyst at Phillip Nova.
"Investors are also eyeing the ripple effects of fresh US sanctions on Russian crude," she added.
Supply concerns have largely been alleviated by major producers raising output and since a ceasefire on June 24 ended the conflict between Israel and Iran.
However, investors are increasingly worried about the global economy amid US trade policy changes.
A weaker US Dollar has provided some backing for crude as buyers using other currencies are paying relatively less.
--Reuters--