Market benchmarks in London and Frankfurt fell, while Shanghai and Tokyo closed down. Hong Kong's main index lost 2.1% as pro-democracy protesters crowded into the territory's airport for a second day. Wall Street futures pointed to a slightly lower open.
Investor anxiety has also been fed by weak economic data in Germany and economic jitters in Argentina.
"The global economy is perched precariously, hoping for a positive inflection, but braced for a stumble," said Vishnu Varathan of Mizuho Bank in a report.
Last week, Trump said he'd be "fine" if the U.S. and China don't go ahead with a meeting next month, dampening investors' hopes for a resolution.
On Wall Street, futures for the Standard & Poor's 500 index and Dow Jones Industrial Average were off 0.1%.
In Asia, the Shanghai Composite Index lost 0.6% to 2,797.26 and Tokyo's Nikkei 225 tumbled 1.1% to 20,455.41. Seoul's Kospi lost 0.8% to 1,925.83 and Sydney's S&P-ASX 200 gave up 0.3% to 6,568.50. Markets in Japan, India and Southeast Asia were reopening following holidays.
Hong Kong's Hang Seng sank as protesters crowded into Chek Lap Kok airport. The airport cancelled all remaining departing flights for a second day after protesters took over the terminals. Flights were also canceled Monday after protesters who are demanding the resignation of the territory's leader and more democratic freedoms filled its main building.
Investors were rattled by a Chinese government statement Monday saying the mostly nonviolent Hong Kong protests "show the sprouts of terrorism" and were an "existential threat" to the population.
Beijing's use of the term terrorism "triggered a wave of risk aversion across global markets," said Stephen Innes of VM Markets in a report.
ENERGY: Benchmark U.S. crude lost 17 cents to $54.76 per barrel in electronic trading on the New York Mercantile Exchange. The contract gained 43 cents on Monday to close at $54.93. Brent crude, used to price international oils, declined 11 cents to $58.46 per barrel in London. It added 4 cents the previous session to $58.57.
CURRENCY: The dollar fell to 105.16 yen from Monday's 105.30 yen. The euro gained slightly to $1.1217 from $1.1214.
Ott reported from Washington.