Around 1330 GMT, London's benchmark FTSE 100 index was down 0.2 percent compared with Friday's close.
In the eurozone, Frankfurt's DAX 30 slipped 0.1 percent and the Paris CAC 40 shed 0.5 percent.
Wall Street stocks moved slightly lower at the opening bell, with the Dow dipping less than a tenth of a percentage point.
The dollar fought back versus the euro and pound, but fell against the yen.
"This week is likely to see focus remain on trade, with (US President Donald) Trump not one to take a back seat and remove himself from the spotlight," noted Craig Erlam, senior market analyst at Oanda trading group.
"Earnings season could provide a welcome distraction from the political theatre of trade wars but even here it's going to feature as tariffs will have an impact on the outlooks of a number of companies and investors will be keen to hear their views."
Ahead of the weekend, Trump attacked Washington's main trading partners for their currency policies.
"China, the European Union and others have been manipulating their currencies and interest rates lower, while the US is raising rates while the dollars gets stronger and stronger with each passing day - taking away our big competitive edge. As usual, not a level playing field," Trump tweeted.
In an interview with US channel CNBC broadcast Friday, Trump threatened to impose taxes on all Chinese imports, saying the US has been "ripped off by China for a long time".
Tokyo's stock market meanwhile dropped 1.3 percent -- falling for a third straight trading day -- as a stronger yen hurt exporters, making their products less competitive abroad and eroding repatriated profits.
Oil markets rose, though analysts cautioned that concerns about the trade dispute would likely weigh on prices in the short to medium term.
Fears that tensions would escalate into a full-blown trade war dominated a meeting of Group of 20 finance ministers and central bankers at the weekend in Buenos Aires.
The final communique from the group of leading economies stressed "the need to step up dialogue and actions to mitigate risks and enhance confidence" as worries have mounted.
EU finance chief Pierre Moscovici warned that "further trade escalation conflicts would negatively affect" all the countries involved, the US included. Protectionism benefits no one, and creates "no winners, only casualties".
International Monetary Fund chief Christine Lagarde agreed, and again spoke out against the tit-for-tat tariffs and urged that "trade conflicts be resolved via international cooperation without resort to exceptional measures".
In corporate action, shares in auto giant Fiat Chrysler skidded lower Monday after its boss of 14 years Sergio Marchionne stepped down at the weekend due to serious health issues.
They were down 2.9 percent in afternoon trading in Milan and dropped 3.7 percent at the opening of trading in New York.
Meanwhile, shares in separately listed Ferrari slumped 5.6 percent in Milan and 4.7 percent in New York.
Meanwhile, shares in budget airline Ryanair fell in London trading as it reported its profit had been squeezed by higher fuel costs and salaries for pilots. With limited visibility on Brexit and mounting tensions with pilots, the company's share price tumbled 5.9 percent.