Asian shares wobbled on Tuesday, US Treasury yields fell and gold rose as weak global manufacturing activity reinforced worries about slowing growth while uncertainties over the prospect of a Sino-US trade deal also hurt sentiment.

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President Donald Trump said on Monday that any trade deal with China would need to be "somewhat tilted" in favour of the United States. The US government also threatened tariffs on $4 billion of additional European Union goods in a long-running dispute over aircraft subsidies.

The US S&P 500 e-mini futures were up 0.1 percent and MSCI's broadest index of Asia-Pacific shares outside Japan added 0.41 percent, helped by a 1.38 percent gain in Hong Kong shares as investors caught up to Monday's global rally. Markets in Hong Kong had been closed on Monday for a public holiday.

But Chinese blue-chips dipped 0.05 percent and Korean shares lost 0.27 percent.

"Euphoria that the trade negotiations are back on the table has probably waned and again the cautious tone is getting hold of the markets going forward," said Prakash Sakpal, an economist with ING in Singapore, adding that a stronger recovery would require more support.

"We need to see a great deal of negotiation progress on the China-US trade war. And we should also see more regional policy stimulus actually kicking in to prevent any further deterioration in economic activity across the region," he said.

Australian shares managed to push up 0.29 percent 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 percent at a meeting later in the day. The central bank's decision is expected at 0430 GMT.

Japan's Nikkei was up 0.11 percent.

Global shares had rallied strongly on Monday after the United States and China agreed on the weekend to restart trade negotiations aimed at resolving their year-long trade war and Washington said it would postpone further tariffs.

The US President Donald Trump also offered concessions, including an easing of restrictions on tech company Huawei.

Yet, with the previous rounds of Sino-US 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.

The fresh US 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 US 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."

WEAK MANUFACTURING

Manufacturing surveys over the past 24 hours underscored those risks. Factory activity in the eurozone shrank faster last month than previously thought, and US manufacturing activity slowed to a near 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 rose 0.44 percent to 26,717.43, the S&P 500 gained 0.77 percent to 2,964.33 and the Nasdaq Composite added 1.06 percent to 8,091.16.

Over recent trading sessions, risk assets have also been held back by tempering of expectations by US Federal Reserve policymakers for aggressive rate cuts at this month's meeting.

"With the easing of Sino-US trade frictions there will certainly be an improvement in downward pressure on the US economy, and the need for the Fed to ease will clearly lessen," analysts at Jianghai Securities said in a note.

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 17.5 percent, from close to 50 percent last week.

The cautious market mood pushed the yield on benchmark 10-year Treasury notes lower to 2.0171 percent, compared with its US close of 2.033% on Monday, while the two-year yield, watched as a gauge of rate expectations, edged down to 1.7751% from a US close of 1.787 percent.

But the safe-haven yen was flat in a quiet currency market, with the dollar buying 108.42, and the euro lost just 0.05 percent to $1.1279. The dollar index, which tracks the greenback against major rivals was unchanged at 96.847.

In commodity markets, worries over the outlook for the global economy weighed on oil. The US crude dipped 0.39 percent to $58.86 a barrel and global benchmark Brent crude was down 0.23 percent at $64.91 per barrel.