The Dow Jones Industrial Average climbed 337.98 points, or 1.12 percent, to 30,523.80. The S&P 500 rose 42.03 points, or 1.14 percent, to 3,719.98. The Nasdaq Composite Index increased 96.60 points, or 0.90 percent, to 10,772.40.
All the 11 primary S&P 500 sectors ended in green, with industrials and materials up 2.36 percent and 1.91 percent, respectively, leading the advance.
Shares of Goldman Sachs rose 2.33 percent after the investment bank delivered stronger-than-anticipated quarterly results.
U.S. drug and consumer products company Johnson & Johnson also reported third-quarter profit and sales that topped expectations. The stock slipped 0.4 percent on Tuesday.
Of the S&P 500 companies that have reported by far, about 70 percent have beaten profit estimates, and 63 percent have beaten revenue estimates, according to FactSet data.
On Monday, Wall Street's major indexes closed higher with the Dow up more than 500 points.
The two-day rally came in the context of a volatile period for markets pressured by multiple headwinds, and analysts warned of continued bumpy ride ahead.
"We do not believe the conditions are in place for a sustained rally, and the risk-reward for markets over the next three to six months is unfavorable in our view," said Mark Haefele, chief investment officer at UBS Global Wealth Management.
"Major central banks look likely to keep tightening rates until the first quarter of 2023; economic growth will likely continue to slow into the start of the new year; and global financial markets are vulnerable to stress while monetary policy continues to tighten," he added.
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