U.S. light crude oil (CLc1) hit a two-month low of $63.59 a barrel before edging back to $64.00, down $1.06, by 0755 GMT. North Sea Brent (LCOc1) was down 36 cents at $73.08 a barrel.
In an escalating trade war with many of its major partners, including China, U.S. President Donald Trump last week pushed ahead with tariffs on $50 billion of Chinese imports, starting on July 6.
China retaliated by slapping duties on American export products, including crude oil.
Benjamin Lu of futures brokerage Phillip Futures said Beijing's retaliation had spooked oil investors:
"These punitive measures on bilateral trade have unnerved investors as it hurts global economic growth," Lu said.
U.S. bank Morgan Stanley said in a note to clients that the trade spat meant economic "downside risks have risen".
U.S. oil exports have boomed in the last two years as shale oil production has surged, with China becoming one of the biggest customers of American crude.
Brent crude hit a 3-1/2-year high above $80 a barrel in May but has since fallen in response to reports that top suppliers Saudi Arabia and Russia are set to increase production.
"Oil prices have sold off over the past three weeks on concerns over higher OPEC production," said U.S. bank Goldman Sachs on Monday, adding that weaker demand from emerging economies and the escalating trade dispute, as well as rising inventories had further weighed on prices.
The producer cartel of the Organisation of the Petroleum Exporting Countries, de-facto led by Saudi Arabia, and some allies including Russia have been withholding output since the start of 2017.
They will meet in Vienna on June 22 to decide forward production policy, with Russia and Saudi Arabia pushing for higher output.
Despite this, Goldman Sachs said "the oil market remains in deficit ... requiring higher core OPEC and Russia production to avoid a stock-out by year-end".
The bank said it expected OPEC and Russian output to rise by 1.3 million barrels per day (bpd) by year-end and by another 0.5 million bpd in the first half of 2019.
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