Futures had surged to a session high after MNSI reported the EU Commission will propose a 6-month debt extension, citing sources.
The European Commission said there was no formal proposal for resolving Greece's debt problems, although talks were intensive ahead of a series of meetings of euro zone finance ministers and EU leaders in Brussels.
"Markets have been driven by this Greek drama and, as it plays out in real time in front of us, anything that looks like we are getting closer in negotiations and resolution is certainly going to be positive here," said Art Hogan, chief market strategist at Wunderlich Securities in New York.
"Anything that makes us believe we can avoid a sloppy Greek exit is going to be a positive for markets overall, and that is where we are at right now."
The Dow Jones industrial average rose 85.03 points, or 0.48 percent, to 17,814.24, the S&P 500 gained 9.84 points, or 0.48 percent, to 2,056.58 and the Nasdaq Composite added 25.29 points, or 0.54 percent, to 4,751.31.
Coca-Cola Co shares climbed 3.7 percent to $42.75 as one of the biggest boosts to the Dow and S&P 500. It reported a better-than-expected profit and sales in North America, its biggest market, rose for the first time in four quarters to offset the impact of a strong dollar on its overseas business.
Starwood Hotels & Resorts Worldwide Inc rose 6.3 percent to $75.74 after the company posted quarterly results and announced plans to spin off its vacation timeshare business.
General Motors said Harry Wilson, a former member of the U.S. auto task force that helped restructure the company in 2009 during its bankruptcy, wants to join the board of directors and have the automaker commit to a $8 billion share buyback program. Its shares gained 2.4 percent to $36.86.
Even with some high-profile earnings misses from multinationals, largely as a result of dollar strength, Thomson Reuters data through Tuesday morning showed 72.7 percent of the 341 S&P 500 companies reporting earnings have topped expectations, above the 69 percent beat rate in the past four quarters.
Aeropostale surged 20.5 percent to $3.18 after the apparel retailer reported better-than-expected holiday sales and boosted its fourth-quarter outlook.
Economic data expected on Tuesday includes December wholesale trade at 10 a.m. EST (1500 GMT). Expectations call for inventories to rise by 0.2 percent while sales are expected to decline by 0.3 percent.
Advancing issues outnumbered declining ones on the NYSE by 1,781 to 761, for a 2.34-to-1 ratio; on the Nasdaq, 1,635 issues rose and 502 fell, a 3.26-to-1 ratio.
The S&P 500 was posting 11 new 52-week highs and 1 new lows; the Nasdaq Composite was recording 20 new highs and 7 new lows.
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