Stocks on Wall Street set fresh record highs before Trump's highly anticipated remarks to the Economic Club of New York, but slowly pared some gains after the speech, which contained no major policy announcements.
Trump touted his administration's economic record in a campaign-style speech but did not announce a venue or date for signing a trade deal with Chinese President Xi Jinping as market speculation had suggested he might.
Rising technology shares helped Wall Street hit record highs while European shares rebounded towards four-year highs. MSCI's gauge of worldwide equity performance <.MIWD00000PUS> climbed to within 1% of a record peak set in January 2018.
Trade-sensitive chipmakers helped push Europe's STOXX 600 up 0.38% as the Philadelphia semiconductor index rose almost 1% but then pared gains to close 0.28% higher.
Overnight in Asia, MSCI's broadest measure of Asia-Pacific shares outside Japan <.MIAPJ0000PUS> climbed 0.5% while Japan's Nikkei <.N225> ended 0.8% higher.
Greg Anderson, global head of foreign exchange strategy at BMO Capital Markets, said Trump's speech had no revelations.
"The only thing that's maybe new is that he did not announce a date and a time for a signing ceremony. Where markets had been hoping for that, those hopes were dashed," Anderson said.
Markets have been focused on a U.S.-China trade deal but improving economic data lately has provided upside too, said Candice Bangsund, a global asset allocation strategist at Fiera Capital in Montreal.
"There's been so much pessimism on the state of the global economy that earnings or fundamentals matter very little when it comes to equity gains this year," Bangsund said.
"Going forward, we expect that fundamentals should prevail. That's going to drive the next up leg."
MSCI's gauge of stocks across the globe <.MIWD00000PUS> gained 0.17%. In Europe, the FTSEurofirst 3000 index <.FTEU3> of leading regional shares closed up 0.42%.
The Nasdaq set a new closing high while the benchmark S&P 500 and Dow Jones industrials hit intraday records.
The Dow Jones Industrial Average closed unchanged at 27,691.49. The S&P 500 gained 4.83 points, or 0.16%, to 3,091.84 and the Nasdaq Composite added 21.81 points, or 0.26%, to 8,486.09.
Investors were anxious about Hong Kong after a violent escalation of protests knocked 3% off the key Hang Seng and nearly 2% off Asia-exposed banks HSBC and StanChart in recent days.
Hong Kong's embattled leader Carrie Lam said protesters who were trying to "paralyse" the city were extremely selfish and that she hoped all universities and schools would urge students not to participate in violence.
U.S. Treasury yields held below three-month highs after Trump's speech.
A holiday in the United States had closed the Treasury market on Monday but there was an early milestone on Tuesday as the gap between short-term 3-month and longer-term 10-year yields hit the widest level of the year so far.
That steepening of the yield curve adds to signs that fears of recession were receding.
"Recession fears are misplaced. We are not ripe for an extended bear market," Bangsund said.
Treasury yields on 10-year notes fell to 1.9173%. European yields were a touch higher.
The dollar was little changed after Trump spoke, remaining mostly higher on the day.
The dollar index rose 0.14%, with the euro down 0.23% to $1.1007. The Japanese yen strengthened 0.07% versus the greenback at 109.00 per dollar.
Gold slipped to its lowest level in more than three months on increased appetite for riskier assets.
U.S. gold futures settled down 0.2% at $1,453.70 per ounce.
Oil prices edged lower after paring gains of about 1%.
U.S. crude fell 6 cents to settle at $56.80 a barrel, while Brent crude futures fell 12 cents to settle at $62.06.
By Herbert Lash