Further dragging on sentiment was the U.S. government's threat on Monday of tariffs on $4 billion of additional European Union goods, in a long-running dispute over aircraft subsidies.
U.S. futures were flat, while MSCI's broadest index of Asia-Pacific shares outside Japan was down in early deals. It last traded up 0.38%, helped by a 1% gain in Hong Kong shares as investors caught up to Monday's global rally. Markets in Hong Kong had been closed Monday for a public holiday.
Australian shares managed to push up 0.27% on expectations that the Reserve Bank of Australia will cut its benchmark cash rate by 25 basis points to a record low of 1.0% at a meeting later in the day.
Japan's Nikkei was flat.
Global shares had rallied on Monday after the United States and China agreed on the weekend to restart trade negotiations aimed at resolving their nearly year-long trade war and Washington said it would postpone further tariffs.
U.S. President Donald Trump also offered concessions, including an easing of restrictions on tech company Huawei.
Yet, with the previous rounds of Sino-U.S. negotiations breaking down in acrimony, investors were now turning to the prospects of actual progress in talks to settle the dispute that has dented global trade, business investment and economic growth.
And the fresh U.S. tariff threats against Europe also point to a worrisome prospect of a broadening trade dispute, said Michael McCarthy, chief markets strategist at CMC Markets in Sydney, in a note to clients.
"The problem is the widening of the dispute. Europe, the U.S. and China account for almost two thirds of global GDP," he said. "An ongoing disruption to trade between these three major economies, prosecuted for domestic political purposes, could sink global growth."
Manufacturing surveys over the past 24 hours underscored those risks. Factory activity in the euro zone shrank faster last month than previously thought, and that U.S. manufacturing activity slowed to near a three-year low in June.
"Global manufacturing PMI took the wind from the sails of risk assets outside of those which are stock related as it becomes apparent this is a real and genuine slowdown the world is experiencing," Greg McKenna, strategist at McKenna Macro, said in a note to clients.
While stocks on Wall Street ended higher, they pared early gains that had seen the benchmark S&P 500 index briefly surpass its previous record high.
The Dow Jones Industrial Average <.DJI> rose 0.44% to 26,717.43, the S&P 500 <.SPX> gained 0.77% to 2,964.33 and the Nasdaq Composite <.IXIC> added 1.06% to 8,091.16.
Over recent trading sessions, risk assets have also been held back by a tempering of expectations by U.S. Federal Reserve policymakers for aggressive rate cuts at this month's meeting.
"At its most recent meeting, the Fed noted that trade frictions had become one of the biggest uncertain factors influencing the outlook for the U.S. economy, and one of the major factors influencing the direction of U.S. monetary policy," analysts at Jianghai Securities said in a note.
"With the easing of Sino-U.S. trade frictions there will certainly be an improvement in downward pressure on the U.S. economy, and the need for the Fed to ease will clearly lessen."
Market expectations that the Fed would implement a relatively large rate cut in July have fallen, with the probability of a 50 basis-point cut at 18.5%, from close to 50% last week.
The cautious market mood pushed the yield on benchmark 10-year Treasury notes lower to 2.0171%, compared with its U.S. close of 2.033% on Monday, while the two-year yield, watched as a gauge of rate expectations, edged down to 1.7792% from a U.S. close of 1.787%.
The safe-haven yen also strengthened, with the dollar dropping 0.05% against the Japanese currency to 108.38
In commodity markets, U.S. crude dipped 0.59% to $58.74 a barrel and global benchmark Brent crude was down 0.43% at $64.78 per barrel.
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