Gains in financial stocks pushed the Dow to a record high and just 20 points short of 20,000, a level it has never touched.
Goldman Sachs, which was up 2.2 percent, gave the biggest boost to the blue-chip index.
Wall Street extended a recent rally on Monday but finished the session short of earlier highs as risk aversion set in following the killing of Russian ambassador to Turkey in Ankara and a truck attack in Germany.
"2016 is ending with tragic incidents in Turkey and Germany, but investors have become so fast in digesting bad news, and this explains the resilience in financial markets," said Hussein Sayed, chief market strategist at FXTM.
U.S. stocks have been on a tear since the Nov. 8 presidential election, with the S&P rising nearly 6 percent on bets that President-elect Donald Trump's plans for deregulation and infrastructure spending will boost the economy.
"We're looking at a higher opening today but the lack of any major economic news and the fact that market shrugged off Monday's events means stocks will drift in an upwards trend," said Peter Cardillo, chief market economist at First Standard Financial in New York.
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At 9:42 a.m. ET (1442 GMT) the Dow Jones industrial average was up 87.78 points, or 0.44 percent, at 19,970.84.
The S&P 500 was up 8.26 points, or 0.36 percent, at 2,270.79.
The Nasdaq Composite was up 24.33 points, or 0.45 percent, at 5,481.78.
Eight of the 11 major S&P sectors were higher, with the financial index's 0.87 percent rise leading the advancers.
Oil prices edged higher on forecasts of a steep draw in U.S. crude oil stocks that could indicate a global oversupply is starting to shrink. [O/R]
The dollar hit a 14-year high as the yen fell after the Bank of Japan stuck to its ultra-loose monetary policy and the euro weakened following deadly attacks in Germany and Turkey.
General Mills fell 2.4 percent to $60.80 after the Cheerios cereal-maker's quarterly results missed expectations.
BlackBerry rose 3.6 percent to $7.99 after the Canadian smartphone maker's adjusted profit beat analysts' estimates.
Nvidia was up 4.2 percent at $106.04 after brokerages Goldman Sachs and Mizuho raised their price targets on the chipmaker's stock.
Advanced Micro Devices was up 3.8 percent at $11.38 after Mizuho raised upgraded the stock to "buy".
Advancing issues outnumbered decliners on the NYSE by 1,827 to 830. On the Nasdaq, 1,668 issues rose and 676 fell.
The S&P 500 index showed 19 new 52-week highs and no new lows, while the Nasdaq recorded 86 new highs and nine new lows.