Brent crude futures were down 71 cents, or 1.15pc, to $61.18 per barrel by 1050 GMT.
US West Texas Intermediate (WTI) crude futures were down 56 cents, or 1.01pc, to $55.10 a barrel.
"The escalation of trade measures only reinforces concerns over global economic growth and hence by extension global oil demand growth," said Harry Tchilinguirian, global oil strategist at BNP Paribas in London.
"(But) supply fundamentals are tightening and are supportive for oil prices."
Both crude benchmarks fell last week, with Brent down 2.5pc and US crude falling 1pc after plummeting by more than 7pc on Thursday after Trump's tweet to the lowest level in about seven weeks.
Asian equity markets dropped to a six-month low on Monday while gold prices climbed as investors sought safe-haven assets.
Trump last week said he would impose a 10pc tariff on $300 billion of Chinese imports starting on Sept. 1 and said he could raise duties further if China's President Xi Jinping failed to move more quickly towards a trade deal.
The announcement extends US tariffs to nearly all imported Chinese products. China on Friday vowed to fight back against Trump's decision, a move that ended a month-long trade truce.
On Monday, China let the yuan tumble beyond the 7-per-dollar level for the first time in more than a decade, in a sign Beijing may tolerate further currency weakness because of the trade dispute.
A lower yuan would raise the cost of dollar-denominated oil imports in China, the world's biggest crude oil importer.
Signs of rising oil exports from the United States also pressured prices on Monday. US shipments surged by 260,000 barrels per day (bpd) in June to a monthly record of 3.16 million bpd, US Census Bureau data showed on Friday.
The US weekly oil rig count, an indicator of future production, fell for a fifth week in a row as most independent producers cut spending even though majors were still pushing ahead with investments in new drilling.
Iran's seizure of an Iraqi oil tanker raised some concerns about potential Middle East supply disruptions in the Gulf, with Iranian state media reporting on Sunday that its Iranian Revolutionary Guards seized the ship for smuggling fuel.