Benchmarks in London, Frankfurt, Tokyo and Shanghai declined and Wall Street drifted toward a lower open.
Traders looked ahead to a meeting between Presidents Donald Trump and Xi Jinping at this week's Group of 20 meeting of major economies in Japan. Forecasters expect the leaders to reassure financial markets by agreeing to revive trade talks without committing to a timeline or other details.
The top U.S. and Chinese negotiators, Trade Representative Robert Lighthizer and Vice Premier Liu He, spoke Monday by phone, according to their governments. No details were released.
The conflict over Beijing's technology ambitions and trade surplus has fed fears it will depress global economic growth. The standoff was triggered by complaints Beijing steals or pressures companies to hand over technology. Both sides imposed tariffs on hundreds of billions of dollars in traded goods. Tensions worsened after Washington tightened sanctions on Chinese tech giant Huawei.
"Both presidents have a very low bar of merely agreeing to resume trade talks, without having to iron out any of the sticking points at the G-20," Chang Wei Liang of Mizuho Bank said in a report.
The realities of achieving a settlement "will probably be relegated to the backseat as the 'feel good' factor of the G-20 displaces caution," Chang said.
London's FTSE 100 lost 0.1% to 7,407 and Frankfurt's DAX was flat at 12,272. France's CAC-40 declined 0.1% to 5,515.
On Wall Street, the futures for the benchmark Standard & Poor's 500 index and the Dow Jones Industrial Average were off 0.1%.
In Asia, the Shanghai Composite Index lost 0.9% to 2,982.07 and Tokyo's Nikkei 225 sank 0.4% to 21,193.81. Hong Kong's Hang Seng was 1.1% lower at 28,185.88. Seoul's Kospi lost 0.2% to 2,121.64 while Sydney's S&P-ASX 200 shed 0.1% to 6,658.00. India's Sensex rose 0.7% to 39,412.80.
Investors have been reassured by statements from the Federal Reserve this month that suggest the central bank is prepared to cut interest rates in response to a slowing global economy. Even so, traders are concerned corporate profits might suffer should the kind of economic slowdown that would prompt the Fed to cut rates take hold.
ENERGY: Benchmark U.S. crude fell 21 cents to $57.69 per barrel in electronic trading on the New York Mercantile Exchange. The contract gained 47 cents on Monday to close at $57.90. Brent crude, used to price international oils, lost 42 cents to $63.76 per barrel in London. It shed 27 cents the previous session to $64.18.
CURRENCY: The dollar declined to 107.03 yen from Monday's 107.29 yen. The euro slipped to $1.1381 from $1.1400.
Matt Ott in Madrid contributed to this report.