Benchmark Brent crude futures were down 69 cents, or 1.1%, at $64.51 a barrel at 1:39 p.m. EDT (1739), while U.S. crude futures shed 5 cents, or 0.1%, to $57.38 a barrel.
Last week, Brent climbed 5% and U.S. crude surged 10% after Iran shot down a U.S. drone on Thursday in the Gulf. This added to tensions stoked by attacks on oil tankers in the area in May and June that Washington has blamed on Iran.
Iran denies any role in the tanker attacks.
U.S. President Donald Trump imposed new sanctions on Iran on Monday, but he earlier called off a retaliatory attack on the Middle East nation at the last minute after the drone was downed.
"I think some of the risk premium that got built in because of U.S. tensions with Iran is easing a bit," said John Kilduff, a partner at Again Capital Management in New York. "I think we're also starting to see the economic concerns and demand concerns re-emerge for the market."
The International Energy Agency (IEA) said this month it had revised down its estimate for crude demand growth in 2019, citing the U.S.-China trade fight.
Weak manufacturing data released on Monday by the Federal Reserve Bank of Dallas, Texas, added to worries about slipping demand for crude oil.
Hopes are waning for progress in Sino-U.S. trade talks at this week's G20 meeting as investors await a meeting between Presidents Donald Trump and Xi Jinping.
"The most important factor weighing on the oil price of late was the fear of a massive slowdown in demand growth, especially in view of the trade conflict between the US and China," Commerzbank said in a note. "We do not expect any agreement to be reached during the meeting between Presidents Trump and Xi during the G20 summit at the end of the week."
Supply still looks to remain relatively tight, as the Organization of the Petroleum Exporting Countries and its allies including Russia, an alliance known as OPEC+, appear likely to extend a deal on curbing output when they meet on July 1-2 in Vienna, analysts said.
Russian Energy Minister Alexander Novak said on Monday that international cooperation on crude production had helped stabilize oil markets and was more important than ever. He also voiced concerns about demand.
(Reporting by Laila Kearney in New York; Additional reporting by Noah Browning in London; Editing by David Gregorio and Matthew Lewis)