Investors were also looking ahead to Friday's meeting of China's legislature for details of possible new steps by Beijing to stimulate its virus-battered economy.
A survey of business managers in the eurozone showed that activity continued to shrink at a rapid pace in May, despite a slight pickup from the historic plunge in April. The publishers of the survey, IHS Markit, said it indicates a 9% drop in GDP this year, with a recovery likely to take years. Investors are "trying to make heads or tails of the recent China trade spats with the U.S. and Australia," Stephen Innes of AxiCorp said in a report.
In Asia, the Shanghai Composite Index lost 0.6% to 2,867.92 and the Nikkei 225 in Tokyo declined 0.2% to 20,552.31. The Hang Seng in Hong Kong lost 0.5% to 24,280.03. Investors are looking to Premier Li Keqiang's speech to China's ceremonial legislature Friday for details of Beijing's spending plans to speed up economic recovery.
"Renewed trade tensions between the U.S. and China could weigh on markets in the coming months," Esty Dwek of Natixis IM said in a report. "Higher volatility is likely, especially as `tough on China' will clearly be a large part of Trump's re-election campaign."