France's CAC 40 was little changed but inching down less than 0.1 percent at 5,349.26 in early trading. Germany's DAX inched down nearly 0.2 percent to 11,639.18. Britain's FTSE 100 dipped 0.4 percent to 7,066.93. US shares were set to drift lower with Dow futures falling 0.2 percent to 25,882. S&P 500 futures were also down 0.2 percent at 2,878.20.
Japan's benchmark Nikkei 225 rose nearly 1.0 percent to finish at 20,456.08. Australia's S&P/ASX 200 added 0.5 percent to 6,471.20, while South Korea's Kospi gained 0.4 percent to 1,924.60. Hong Kong's Hang Seng fell 0.3 percent to 25,613.07. The Shanghai Composite added 1.4 percent to 2,902.19.
"It remains all about trade as President Donald Trump's comments on the matter had once again been the primary driver for markets at the start of the week. Even though the sentiment had taken a positive turn on the latest update, uncertainty nevertheless persists to warrant a more cautious stance," said Jingyi Pan, market strategist at IG in Singapore.
Monday's rally on Wall Street got its start early after President Donald Trump said his negotiators had received encouraging calls from China on Sunday, though China's foreign ministry denied knowledge of any such calls.
The major US indexes are each on track for losses of three percent or more in August in what has been a volatile month for the market as investors try to gauge whether trade conflicts and slowing economies around the world will drag the US into a recession.
On Friday, China announced new tariffs on $75 billion in US goods. Trump responded angrily on Twitter, at one point saying he "hereby ordered" US companies with operations in China to consider moving them to other countries, including the US.
Analysts say uncertainties are bound to remain on global markets as long as Trump continues to send conflicting messages.
"The bigger picture is that deep-seated issues are unlikely to be resolved on the flick of a switch or tweet," said a report from the Asia & Oceania Treasury Department of Mizuho Bank.
Trump later announced the US would increase existing tariffs on $250 billion in Chinese goods to 30 percent from 25 percent, and that new tariffs on another $300 billion of imports would be 15 percent instead of 10 percent.
Global markets appeared headed for another wave of selling early Monday, when indexes in Asia closed lower, until Trump said his trade negotiators had received two "very good calls" from China.
During a news conference in France after the Group of Seven industrialized nations' meeting, Trump said "China wants to make a deal, and if we can, we will make a deal."
Benchmark crude oil rose 29 cents to $53.93 a barrel. It fell 53 cents to settle at $53.64 a barrel. Brent crude oil, the international standard, rose 35 cents to $59.05 a barrel.
The dollar fell to 105.71 Japanese yen from 105.88 yen on Monday. The euro weakened to $1.1102 from $1.1118.