The Dow Jones Industrial Average rose 186.45 points, or 0.56 percent, to 33,704.10. The S&P 500 increased 27.16 points, or 0.70 percent, to 3,919.25. The Nasdaq Composite Index climbed 106.98 points, or 1.01 percent, to 10,742.63.
Ten of the 11 primary S&P 500 sectors ended in green, with communication services and consumer discretionary up 1.29 percent and 1.26 percent, respectively, outpacing the rest. Consumer staples slipped 0.16 percent, the lone declining group.
The December U.S. consumer price index is set for release on Thursday.
"Another report showing inflation continuing to decline, as expected, should be cheered. But if it ticks higher vs. last month, that could weigh on the market," Kevin Matras, executive vice president at Zacks Investment Research, said in a note on Tuesday.
On Monday, U.S. equities gave up earlier gains to end mixed after top Fed officials reiterated a more hawkish line on the outlook for rates.
"We continue to believe that markets have moved too quickly to position for an inflection point in Fed policy, and that conditions are not yet in place for a sustained equity rally," cautioned UBS analysts.
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