U.S. stocks ended higher after volatile trading Tuesday, as Wall Street tried to recover from a sharply lower start to the year amid falling oil prices.

The Dow Jones Industrial Average rose 117.65 points, or 0.72 percent, to 16,516.22. The S&P 500 added 15.01 points, or 0.78 percent, to 1,938.68. The Nasdaq Composite Index increased 47.93 points, or 1.03 percent, to 4,685.92.

Oil prices continued to drop on Tuesday as oversupply worries persisted. The U.S. oil traded below 30 U.S. dollars a barrel for the first time since December 2003 in the afternoon session, but then pared part of losses to end at 30.44 dollars a barrel.

Brent crude for February delivery decreased 69 cents to close at 30.86 dollars a barrel on the London ICE Futures Exchange.

Oil prices have tumbled about 17 percent since the start of the year, dragged lower by a global supply glut and a strong U.S. dollar.

In corporate news, Aluminum company Alcoa unofficially kicked off the fourth-quarter earnings season of 2015 after Monday's closing bell, by reporting earnings that beat estimates but revenue shy of forecast. Alcoa's shares plunged 9 percent to 7.28 dollars apiece on Tuesday.

According to Thomson Reuters, the blended earnings of the S&P 500 companies in the fourth quarter of 2015 are expected to decline 4.7 percent year on year, while the revenue is forecast to decrease 3.3 percent.

On the economic front, the number of job openings was little changed at 5.4 million on the last business day of November, the U.S. Labor Department reported Tuesday.

Overseas, the Chinese currency, the yuan, showed signs of stabilization Tuesday. The central parity rate of the yuan against the U.S. dollar was little changed at 6.5628 Tuesday, according to the China Foreign Exchange Trading System.

Chinese stocks closed slightly higher in the day, with the benchmark Shanghai Composite Index gaining 0.2 percent to close at 3,022.86 points.

European equities rebounded broadly on Tuesday despite the continued decline in oil prices, with French benchmark index CAC 40 rising 1.53 percent.

The CBOE Volatility Index, often referred to as Wall Street's fear gauge, fell 7.53 percent to end at 22.47 Tuesday.

In other markets, the U.S. dollar gained Tuesday as market expected the Federal Reserve to continue the interest rate hike in 2016.

In late New York trading, the euro moved down to 1.0856 dollars from 1.0875 dollars in the previous session. The dollar bought 117.59 Japanese yen, higher than 117.5 yen of the previous session.

Gold futures on the COMEX division of the New York Mercantile Exchange fell on Tuesday as the U.S. dollar showed strength and global markets improved.

The most active gold contract for February delivery moved down 11 dollars, or 1 percent, to settle at 1,085.20 dollars per ounce.