The trade war has yet to have a direct impact on oil markets, but China has indicated it could place tariffs on USA crude imports.
Oil was mixed last week as a Canadian supply outage supported USA crude prices, while an increase in production from Opec's biggest exporter Saudi Arabia pushed Brent lower.
Brent was also being pressured by expectations of higher Saudi and Russian Federation productions, which impact Europe and Asia, where Brent is the benchmark, more than the markets dominated by the U.S. crude prices.
USA crude CLc1 slipped 2 cents to $72.92.
International Brent crude oil futures LCOc1 fell 27 cents, or 0.4 percent, to $77.12 per barrel by 0124 GMT from their last close.
American crude shipments to China now stand around 400,000 barrels per day (bpd), worth around $1 billion a month at current market prices. He also said that he is thinking of slapping additional duties on $500 billion in Chinese goods if Beijing retaliates.
China has indicated that it could place a tariff of 25% on USA oil.
An executive from China's Dongming Petrochemical Group said he expected Beijing to soon impose the tariff on USA oil imports.
South Korea is the world's fifth-largest crude oil importer, and diversity of supplies is vital.
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OPEC and its allies agreed earlier this month to a modest increase in output to dampen the oil price rally, which hit a 3-1/2 year high.
Amid all this, traders were still careful over the trade spat between the United States and China.
US tariffs on $34 billion in Chinese imports took effect as a deadline passed on Friday.
Energy consultancy FGE on Friday issued a stark warning of looming supply shortages due to USA sanctions against Iran, and because of disruptions elsewhere.
"Iran's exports are some 2.7-million barrels a day, including condensate", it noted.
USA investment bank Jefferies said on Friday it expected a drop in Iranian exports well in excess of 1 million bpd due to the US sanctions.
The Korean government, the sources said, had pressured refiners into suspending orders for July shipments of Iranian crude, which is the first time this has happened since 2012, Reuters notes.
The move came as Seoul started negotiations with Washington to seek authorizations over buying Iranian oil, in line with a waiver it received during previous sanctions, the report added.
"At the same time, Venezuela can do nothing to stop its own production decline and will lose another 400,000 bpd by year-end with production going to below 1 million bpd", FGE said, adding that another 300,000 bpd of Libyan capacity was disrupted.
In addition to reducing the price of its August barrels, Saudi Arabia also told the Organization of the Petroleum Exporting Countries (OPEC) that it increased production by nearly 500,000 barrels per day last month.