The S&P 500 climbed 1.2%, the Dow Jones Industrial Average added 238 points, or 1.35%, and the Nasdaq gained 1.7%.
Alcoa kicked off earnings season on a good note after the bell Monday, reporting fourth-quarter earnings and revenue that beat expectations. The aluminum producer forecasts a 7% increase in use of the metal this year, driven by the aerospace and auto industries.
"It will be the first real chance we get to see the effect factors such as the strengthening U.S. dollar, depressed energy prices, and a global slowdown have had on individual companies," Raymond James analyst Andrew Adams said of the beginning of the earnings season. "Energy companies, which make up about 11% of S&P 500 earnings, are expected, not surprisingly, to be a major drag on the aggregate profits."
Energy companies are expected to see profits drop 19.1% year over year, according to FactSet. All S&P 500 companies' profits are forecast to increase 1.1%, its slowest pace of growth in two years on the fall in oil and a stronger U.S. dollar.
IHS (IHS) gained 6.7% as fourth-quarter earnings of $1.68 a share beat estimates by 13 cents and revenue climbed 4% year over year, while KB Home (KBH) - Get Report jumped 1.2% after reporting a 29% increase in quarterly revenue.
West Texas Intermediate continued to crumble overnight after the United Arab Emirates reiterated it will not reduce production in the face of global oversupply and faltering demand from key regions including China and Europe.
"The strategy will not change," said UAE Oil Minister Suhail bin Mohammed al-Mazroui. "We are telling the market and other producers that they need to be rational." OPEC has been reluctant to cut output lest the member countries lose market share. OPEC will gather in June for its next scheduled meeting.
WTI was down 0.87% to $45.67, bouncing back from losses of more than 3% earlier Tuesday. Since last summer, oil prices have dropped nearly 60%.
Stock markets tumbled on Monday as crude oil prices cratered more than 5%. The S&P 500 closed 0.8% lower, clawing back from session lows of more than 1% suffered earlier in the day. The Dow dropped 0.53%, and the Nasdaq tumbled 0.84%.
Jobs opening rose to 4.97 million on the last business day of November, higher than 4.83 million in October, according to the Labor Department's Job Openings and Labor Turnover Survey. Economists had expected a slower pace of growth to 4.88 million for the month.
European markets were higher on speculation of what widely anticipated monetary stimulus might entail. The European Central Bank, which meets next Thursday, has reportedly earmarked 500 billion euros for government bond purchases.
In the U.K., inflation dropped to a 14-year low, falling 0.5% in December from 1.1% in November. Last week, the broader eurozone region reported a slip into a deflationary environment with consumer prices down 0.2% in December from a year earlier.
Amazon (AMZN) - Get Report shares were up 3% on an upgrade to "buy" from Citigroup. "We believe Amazon's valuation represents a good risk/reward as we see valuation support near $300 and upside to at least $354 without assuming multiple expansion," analysts said.
MetLife (MET) - Get Report was slightly higher on news the largest life insurer in the U.S. will file a lawsuit against federal regulators in a challenge to their "too-big-to-fail" designation. The company said the tougher oversight would make its offerings more expensive with little benefit to its fiscal stability.
Philips (PHG) - Get Report fell 1.2% following a warning that full-year earnings will be reduced by about 225 million euros. The Netherlands-based medical equipment company said the hit was due to legal charges and the impact of foreign exchange.
RadioShack (RSH) was more than 22% higher after receiving a financing offer from Salus Capital. The $500 million offer expires Thursday.
--Written by Keris Alison Lahiff in New York.