The Dow Jones Industrial Average jumped 337.76 points, or 1.13 percent, to 30,199.31. The S&P 500 rose 47.13 points, or 1.29 percent, to 3,694.62. The Nasdaq Composite Index increased 155.02 points, or 1.25 percent, to 12,595.06.
All the 11 primary S&P 500 sectors climbed, with utilities and energy both closing up more than 1.9 percent, leading the gains.
U.S.-listed Chinese companies traded mostly higher, with six of the top 10 stocks by weight in the S&P U.S. Listed China 50 index ending the day on an upbeat note.
Top U.S. congressional leaders met on Tuesday to discuss coronavirus relief and government funding, according to the media.
On Monday, a bipartisan group of U.S. lawmakers unveiled its two-part 908-billion-U.S.-dollar COVID-19 relief package as many Americans are set to lose pandemic relief benefits by the end of the year.
The proposal includes a bill that outlines a wide range of relief spending totaling 748 billion dollars, and another piece that provides 160 billion dollars to state and local governments with COVID-19-related liability protections.
Democratic and Republican lawmakers have been deadlocked for months over the size and scope of the next relief package.
Without a new relief package, many Americans will soon lose their unemployment benefits and begin to face hardships like eviction and foreclosure by the end of the year.
The United States has registered more than 16.6 million confirmed cases with related deaths topping 302,600 as of Tuesday afternoon, showed a tally by Johns Hopkins University.
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