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The major futures indexes are indicating a rise of 0.5 percent when Wall Street begins trading on Wednesday.
In Europe, London's FTSE edged up 0.4 percent, Germany's DAX added 0.8 percent and France's CACgained 0.4 percent.
In Asia, Japan's Nikkei 225 rose 0.7 percent, Hong Kong's Hang Seng added 0.9 percent and China's Shanghai Composite also rose 0.9 percent.
China reported 97 more deaths from the coronavirus, pushing the total dead past 1,100.
The number of cases worldwide is about 45,000, all but a few hundred in China.
|I:DJI||DOW JONES AVERAGES||29398.08||-25.23||-0.09%|
|I:COMP||NASDAQ COMPOSITE INDEX||9731.17573||+19.21||+0.20%|
Investor sentiments in Asia were also cheered somewhat by Wall Street, where modest gains overnight nudged the S&P 500 and Nasdaq to all-time highs for the second straight day. The Dow Jones Industrial Average finished essentially flat.
Investors weighed another batch of mostly solid company earnings reports.
Sprint soared after a federal judge cleared a major obstacle to the company being acquired by T-Mobile.
Cruise operators, hotels and other companies that focus on travel made solid gains, the latest sign that traders are feeling less worried about the economic impact from the virus outbreak.
Investors are also getting some encouragement from Federal Reserve Chairman Jerome Powell's comment in a report to Congress, that it was too early to assess the threat the virus poses to the U.S. economy, but he noted that the economy “is in a very good place” with strong job creation and moderate growth.
The Associated Press contributed to this article.