Stocks close up more than 1% on oil; Dow jumps 300 points

U.S. stocks rallied on Tuesday to close up more than 1 percent higher in a second consecutive day of gains, boosted by a surge in oil prices and alleviation of concerns in the euro zone.

"We've got a continuation of strength. Looks like the two major drivers of yesterday's strength are still with us today," said Art Hogan, chief market strategist at Wunderlich Securities.

With Monday's and today's gains, the Dow, S&P and Nasdaq each regained about 70 percent or more of January losses. The Dow Jones Industrial Average (Dow Jones Global Indexes: .DJI) surged 305.3 points in the last 15 minutes of trade to close up 1.76 percent at 17,666.40. All blue chips advanced, led by Caterpillar (CAT)'s nearly 4 percent gain. Exxon Mobil (XOM) and Chevron (CVX) followed, each rising nearly 3 percent or more. "With crude between $50 and $55, a lot of people are going to see Caterpillar as cheap," said Marc Chaikin, CEO of Chaikin Analytics.

Read More Oil spikes 7% to above $53 after BP capex cut Oil extended the past few days' gains to settle up $3.48, a 7 percent surge, to $53.05 a barrel, the highest settlement of 2015. WTI crude is up 22 percent from its intraday low of $43.58 last Thursday. Encouraged, the Dow Transports closed up 1.46 percent, with only the airlines declining. We're "obviously seeing a rebound in some of the oil sector," said Randy Frederick, managing director of trading and derivatives at Charles Schawb. "Overall the market has been weak, until late yesterday, so it'll be interesting to see if it holds up." The Nasdaq underperformed the major indices, with Apple (AAPL) in the red for much of the day. Biotech declines also put pressure on the S&P. Hogan was not concerned about the divergent performance. "You've got a consistently stabilizing energy market," he said. That "broader type move is more impactful on the Dow and the S&P than the Nasdaq." The energy sector closed up 2.78 percent to lead advancers on the S&P 500 for 4 straight days of gains. Firming oil prices and news out of Greece cheered U.S. markets into the close on Monday, putting the S&P 500 above 2,000 points in the close and the Dow up nearly 200 points.

The S&P closing above that key level is "significant," said Peter Cardillo, chief market economist at Rockwell Global Capital. "Perhaps it will set the stage for less volatility in the month of February and more tranquility as the ECB launches its quantitative easing program." Read More Gartman: Germany won't let Greece leave euro zone Greece's Finance Minister Yanis Varoufakis unveiled proposals on Monday to end the confrontation with its creditors by swapping outstanding debt for new growth-linked bonds, the Financial Times reported. On Tuesday, Greek Finance Minister Yanis Varoufakis met with his Italian counterpart in Rome. "This is a back and forth that's going to go on for a while," Frederick said. "The question is where it may go. We've got several weeks before we find out what happens." Back in the United States, Minneapolis Fed President Narayana Kocherlakota reiterated on Tuesday that the Federal Reserve should keep interest rates near zero this year, or risk slowing U.S. job growth and inflation's return to the U.S. central bank's 2-percent goal. Earlier, St. Louis Federal Reserve Bank President James Bullard downplayed the Fed's nod to international developments in its latest policy statement, saying it was simply an acknowledgement of constant U.S. central bank discussion on the potential impact of global market events. Bullard repeated his view that the Fed needs to raise rates sooner and then move gradually higher after that. He also said that the oil price plummet is distorting market-based inflation expectation measures, and that these measures should be set aside until energy prices stabilize.

Factory orders for December posted a greater-than-expected decline of 3.4 percent. Analysts expected a decline for the month, especially with Monday's weaker ISM manufacturing numbers. A smaller-than-previously reported drop in business spending plans supported a likely rebound in the months ahead. January auto sales topped expectations and encouraged analysts. "If you were concerned, I think the consumer is spending on bigger ticket items," Hogan said. U.S. futures gained on Tuesday, following European and Asian bourses higher as oil prices rebounded.

Read More These stocks will benefit from the stronger dollar Reporting before the bell, UPS (UPS) matched estimates with adjusted quarterly profit of $1.25 per share, while revenues were above forecasts. However, the company said its results were below its own expectations, and it also forecast full-year results below Street forecasts. It plans to address these issues with cost and revenue actions, although UPS adds that customers were "delighted" with its service during the holiday season. BP (London Stock Exchange: BP.-GB) posted better-than-expected replacement cost profit of $2.2 billion for the fourth quarter, despite taking a $3.6 billion impairment cost. In a television interview, CEO Bob Dudley warned that oil prices could remain as low as $50 per barrel " for some time ." London-listed shares of BP rose as much as 4 percent after the results were out.

Things heat up later in the day with results from Disney, as well as Gilead Sciences.

The S&P 500 (^GSPC) closed up 29.18 points, or 1.44 percent, at 2,050.03, with energy leading gains across all sectors. The Nasdaq (^IXIC) closed up 51.05 points, or 1.09 percent, at 4,727.74. The major indices are still down for the year. The CBOE Volatility Index (^VIX) (VIX), widely considered the best gauge of fear in the market, traded just above 17. Four stocks advanced for every decliner on the New York Stock Exchange, with an exchange volume of 972 million and a composite volume of nearly 4.6 billion in the close. The U.S. 10-year Treasury (U.S.:US10Y) yield rose to 1.78 percent. The U.S. dollar edged slightly higher against major world currencies after a significant decline for much of Tuesday.

Gold futures closed down $15.30 at $1,260.30 an ounce. -Reuters contributed to this report.

On tap this week:Tuesday Earnings: Disney (DIS), Gilead Sciences (GILD), Aflac (AFL), CH Robinson (CHRW), Chipotle Mexican Grill (CMG), Edwards Lifesciences (EW) Wednesday Earnings: General Motors (GM), GlaxoSmithKline (London Stock Exchange: GSK-GB), Merck (MRK), Toyota Motors (Tokyo Stock Exchange: 7203.T-JP), Automatic Data (ADP), Boston Scientific (BSX), Clorox (CLX), Humana (HUM), Marathon Petroleum (MPC), Motorola Solutions (MSI), Ralph Lauren (RL), Sony (Tokyo Stock Exchange: 6758.T-JP), Whirlpool (WHR), 21st Century Fox (FOXA), Allstate (ALL), CBRE Group (CBG), Everest Re (RE), Keurig Green Mountain (GMCR), Lincoln National (LNC), Prudential Financial (PRU), Under Armour (UA), Weatherford International (WFT), Yum Brands (YUM) 7:00 a.m.: Mortgage applications 8:15 a.m.: ADP Employment report 9:45 a.m.: PMI Services Index 10:00 a.m.: ISM non-Manufacturing Index 10:30 a.m.: Oil inventories 12:45 a.m.: Fed's Mester speaks Thursday Earnings: AstraZeneca (London Stock Exchange: AZN-GB), BNP Paribas (Euronext Paris: BNP-FR), Daimler (XETRA:DAI-DE), Philip Morris (PM), Sanofi (Euronext Paris: SAN-FR), Michael Kors (KORS), Sirius XM Radio (SIRI), Sprint (NYSE:S), TevaPharma (Tel Aviv Stock Exchange: TEVA-IL), Activision Blizzard (ATVI), CME Group (CME), Expedia (EXPE), GoPro (GPRO), LinkedIn (LNKD), McKesson (MCK), News Corp. (NWSA), Nuance Communications (NUAN), Symantec (SYMC), Twitter (TWTR), Buffalo Wild Wings (BWLD), Lionsgate (LGF), Pandora (NYSE:P), Tempur Sealy (TPX), Yelp (YELP) 5:00 a.m.: Fed's Rosengren speaks 7:30 a.m.: Challenger Job-Cut report 8:30 a.m.: International trade 8:30 a.m.: Jobless claims 8:30 a.m.: Productivity & costs 10:30 a.m.: Natural gas inventories 3:00 p.m.: Treasury STRIPS 4:30 p.m.: Fed balance sheet/Money supply Friday Earnings: Moody's (MCO) 8:30 a.m.: Nonfarm payrolls 12:45 p.m.: Fed's Lockhart speaks 3:00 p.m.: Consumer Credit More from CNBC.com: How to rent the Apple Watch before buying it Uber to develop driverless cars in Google challenge Shopping smart for health care? Good luck with that