Analysts have said markets are overdue for a downward correction but stocks found support from two home price reports released Tuesday that indicated the housing market finished 2012 with strong gains.
The Federal Housing Finance Agency said home prices rose 1.4 percent in the fourth quarter over the third quarter. The S&P/Case-Shilling home price report said its national composite index posted a gain of 7.3 percent on the year.
By close of trading, stocks had regained about half of Monday's rout.
The Dow Jones industrial average added 115.96 points or 0.84 percent to 13,900.13. The Standard and Poor's 500 added 9.09 points or 0.61 percent to 1,496.94. The Nasdaq composite added 13.40 points or 0.43 percent to 3,129.65.
On the New York Stock Exchange, 2,030 stocks advanced and 1,003 declined on a volume of 3.9 billion shares traded.
The 10-year U.S. treasury fell 5/32 to yield 1.885 percent.
Against the dollar the euro fell to $1.3058 from Monday's $1.3062. Against the yen, the dollar was higher at 91.98 yen from 91.82 yen.
In Tokyo, the Nikkei 225 closed at 11,398.81 points, down 263.71 points or 2.26 percent.
In London, the FTSE 100 index shed 1.34 percent, 84.93 points, to 6,270.44.