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The major futures indexes are indicating a rise of 4 percent when trading begins.
In Europe, London's FTSE rose 2.5 percent, Germany's DAX gained 3.6 percent and France's CAC added 3.2 percent.
Asian markets were also rising. Japan's Nikkei gained 2 percent, Hong Kong's Hang Seng added 2.1 percent, while China's Shanghai Composite jumped 2 percent.
China on Tuesday reported no new deaths from the coronarivus over the past 24 hours and had 32 new cases, all from people who returned from overseas.
The country that gave rise to the global pandemic has recorded 3,331 deaths and 81,740 total cases. Numbers of daily new deaths have been hovering in the single digits for weeks, hitting just one on several occasions.
The number of new coronavirus cases is dropping in the European hotspots of Italy and Spain. The center of the U.S. outbreak, New York, also reported its number of daily deaths has been effectively flat for two days.
Investors have been waiting anxiously for signs that the rate of new infections may be hitting its peak, which would give some clarity about how long the upcoming recession will last and how deep it will be. Without that, markets have been guessing about how long businesses will remain shut down, companies will lay off workers and flights remain canceled due to measures meant to slow the speed of the outbreak.
|I:DJI||DOW JONES AVERAGES||34200.67||+164.68||+0.48%|
The S&P 500 climbed 175.03, or 7 percent and nearly all the stocks in the index were higher.
The Dow Jones Industrial Average shot up 1,627.46 points, or 7.7 percent to 22,679.99, and the Nasdaq rose 7.3 percent.
Japan announced a $1 trillion package to support the world’s third-largest economy, including cash handouts to needy families and help for small businesses. Prime Minister Shinzo Abe announced a state of emergency that will ramp up precautions meant to curb the rapid spread of the virus.
Benchmark U.S. crude added 3.5 percent or 92 cents to $27.03 a barrel. It fell $2.26, or 8 percent, to settle as $26.08 a barrel after surging nearly $7 last week. It started the year above $60 per barrel. Brent crude, the international standard, rose 96 cents to $34.01 a barrel.
The Associated Press contributed to this article.