Decliners were a step ahead of advancers on the New York Stock Exchange, with an exchange volume of 780 million and a composite volume of 3.3 billion in the close, the third lowest volume day this year.
High-frequency trading accounts for about 47.5 percent of trade volume this year, down from a peak of 61 percent in 2009, according to TABB Group estimates.
U.S. markets were closed on Monday for the Presidents' Day holiday.
U.S. stocks closed near highs on Friday, with the S&P setting its first record for 2015 at 2,096.99 and the Dow Jones industrial average above 18,000 for the first time since December.
Prime Minister Alexis Tsipras said on Tuesday that his Syriza party would not compromise with the euro zone on terms that he called "blackmail." On Monday, Greece failed to come to a settlement over a proposal for a six-month extension of its international bailout package.
"I think the biggest thing is the market is not worried about Greece talks," said Doug Cote, chief market strategist at Voya Investment Management,. "Greece has the most to lose. They have more incentive to get it done."
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On Wednesday, the European Central Bank will discuss Greek banks' use of emergency liquidity assistance (ELA)—and after which the ECB may give more clarity as to when or whether it will put a cap on its funding for Greek banks.
"The underlying assumption in the market place is that something will get done, albeit in the 11th hour," said Art Hogan, chief market strategist at Wunderlich Securities.
European shares closed mixed on Tuesday, with the Athens Stock Exchange down about 2.5 percent as banks weighed heavily on the index.
Oil prices continued to firm, with crude settling up 75 cents to $53.53 a barrel on the New York Mercantile Exchange.
"We don't need it to go up or down, we just need it to stabilize," said Randy Frederick, managing director of trading and derivatives at Charles Schwab.
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In other overseas news, fighting intensified in eastern Ukraine past the agreed deadline of a cease-fire with Russia on Sunday.
The New York Fed's Empire State general business conditions index fell in February to 7.78 from January's reading of 9.95.
Although the reading missed expectations, Cote said it was "pretty good" and "could have been a lot worse."
The NAHB housing market indices showed U.S. home builder sentiment fell 2 points, largely due to the frigid weather, the National Association of Home Builders said on Tuesday.
December's TIC capital flows data comes at 4:00 p.m. ET.
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Medtronic reported earnings that beat on both the top and bottom lines, noting that the results were above the firm's own forecast.
Transocean's CEO Steven Newman stepped down and will be replaced on an interim basis by chairman Ian Strachan. The oilfield services company also slashed its annual dividend by 80 percent, to 60 cents per share from the prior $3.
Agilent, Analog Devices, CF Industries, Devon Energy, Fossil and FirstEnergy are among the firms reporting after the bell.