KEEPING SCORE: Germany's DAX added 1.3 percent to 10,944.12 while the CAC 40 in France climbed 1.4 percent to 4,837.95. Britain's FTSE 100 jumped 0.8 percent to 6,913.33. Wall Street looked set for more gains, with the future contract for the Dow up 0.5 percent while that for the S&P 500 also rose 0.5 percent.
ASIA'S DAY: Japan's Nikkei 225 index gained 1.1 percent to 20,427.06 and Hong Kong's Hang Seng jumped 2.3 percent to 26,462.32. The Shanghai Composite index surged 1.0 percent to 2,544.34 while South Korea's Kospi advanced 2.0 percent to 2,064.71. Australia's S&P ASX 200 surged 1.0 percent to 5,778.30. Shares also rose in Taiwan and Southeast Asia.
CHINA-US TRADE: The Chinese Foreign Ministry said trade talks with the U.S. in Beijing had ended after three days of discussions. It gave no details. President Donald Trump tweeted overnight that "Talks with China are going very well!" a potential positive sign even though no major developments had been announced. Experts say it may take months to resolve the causes of the trade war, which include disagreements over Beijing's handling of technology and intellectual property.
US SHUTDOWN: President Donald Trump's televised address Tuesday night helped soothe frazzled nerves over what steps he might take in the standoff with lawmakers over border wall funding, which has resulted in a partial government shutdown. Trump argued for funding on security and humanitarian grounds as he sought to put pressure on newly empowered Democrats.
ANALYST'S VIEWPOINT: "Trump did not declare a national emergency, nor did he hint toward one, which might have been a fear before the speech," Stephen Innes of Oanda said in a commentary. Meanwhile, "currencies are holding firm riding the wave sentiment from the positive buzz in U.S.-China trade talks."
ENERGY: Oil prices also continued to rally. U.S. crude rose $1.05 to $50.83 per barrel in electronic trading on the New York Mercantile Exchange. It has risen for eight of the past nine days and gained 2.6 percent to $49.78 per barrel on Tuesday. Brent crude, used to price international oils, added $1.06 to $59.78 per barrel. It gained 2.4 percent to $58.72 a barrel in London.
CURRENCIES: The dollar climbed to 108.90 yen from 108.75 yen. The euro rose to $1.1461 from $1.1442.
AP Markets Writer Marley Jay contributed. He can be reached at http://twitter.com/MarleyJayAP