Stocks rose slightly after the open on Tuesday following steep losses in the previous session, with gains capped by resurfacing worries about the euro zone's ability to contain its debt crisis.

The Dow Jones industrial average rose 46.39 points, or 0.36 percent, to 12,973.56. The S&P 500 Index rose 2.26 points, or 0.17 percent, to 1,369.20. The Nasdaq Composite Index inched up 0.51 point, or 0.02 percent, to 2,970.96.

(Reporting by Edward Krudy; editing by Jeffrey Benkoe)