The pan-European STOXX 600 benchmark was down 0.1 percent, pulling back from a one-week high hit in the previous session.
Japan's Nikkei managed to add 0.65 percent and Chinese blue chips rose 0.4 percent.
MSCI's broadest index of Asia-Pacific shares outside Japan was last up 0.4 percent. E-Mini futures for the S&P 500 dipped 0.1 percent and spreadbetters pointed to a subdued start for the major European Bourses.
The MSCI All-Country World Index, which tracks shares across 47 countries, was up less than 0.1 percent.
In an interview with the Wall Street Journal, Trump said he expects to raise tariffs on $200 billion in Chinese imports to 25 percent from 10 percent currently. He said it was "highly unlikely" he would accept China's request to hold off on the increase, planned for Jan. 1.
The comments ran counter to recent speculation about a possible deal when Trump meets Chinese President Xi Jinping at the G20 summit in Buenos Aires later this week.
"The upcoming meeting between Trump and Xi is pivotal going into the year-end and for the outlook for global growth, which has shown signs of slowing," said Lee Hardman, a currency analyst at MUFG in London.
"If there's no breakthrough, that makes it more likely that more tariffs will be imposed, and that increases downside risks to trade."
The news initially put trade-sensitive currencies, including the Australian dollar, on the defensive, although it climbed back into positive territory in European trade. The dollar was flat against the yen at 113.615
The index that measures the dollar against a basket of other currencies was up 0.2 percent.
Sterling was weaker across the board after Trump said on Monday the agreement allowing the United Kingdom to leave the European Union may make trade between Washington and London more difficult.
The euro edged lower to $1.1319.
OIL SHIFTS RISKS ON INFLATION, FED Shares in Apple Inc fell after hours in reaction to Trump's comments that tariffs could also be placed on laptops and iPhones imported from China.
Trump's remarks came just as the mood among investors had shown signs of brightening and Wall Street took heart from an upbeat holiday shopping period.
The Dow had ended Monday up 1.46 percent, the S&P 500 gained 1.55 percent and the Nasdaq 2.06 percent.
The rally came after the S&P 500 on Friday recorded its lowest close in six months, down more than 10 percent from September's peaks and back in "correction" territory.
In commodity markets, oil prices were depressed by record Saudi Arabian production even as the kingdom tried to persuade other exporters to agree output cuts ahead of an OPEC meeting next week. Oil had climbed nearly 3 percent on Monday but that was seen as largely a technical correction after weeks of heavy losses, driven both by oversupply and demand worries.
US crude was off 1.38 percent at $50.92 a barrel, while Brent futures were down 1 percent to $59.83.
Analysts at National Australia Bank noted the 30 percent drop in oil since early October would drag on US inflation in coming months, perhaps offering further reason for the Federal Reserve to go slower on tightening.
"This is a starkly different picture to just a few months ago," said NAB's market strategist Tapas Strickland. "A stable to lower inflation outlook means there is no urgency for the Fed to hike rates. An early 2019 pause is thus becoming more probable."
The futures market has already shifted to imply two more hikes at most next yea. The Fed itself is predicting three, and more in 2020.
Hints on rate moves may come from Fed Vice Chairman Richard Clarida, who speaks later on Tuesday, and Chair Jerome Powell, who will make an appearance the day after.