Stocks added to strong gains as financial stocks soared, and as volatility in the oil markets eased amid news OPEC is considering a boost in output.
TheDow Jones Industrial Average rose more than 130 points, reversing losses from Monday triggered by worries over the situation in the Middle East.
Among Dow components, Bank of America , American Express and JPMorgan gained, while McDonald's and Intel fell.
The S&P 500 rose more than 1 percent to about 1,323, while the Nasdaq also rose more than 1 percent. The CBOE Volatility Index, widely considered the best gauge of fear in the market, fell to below 20.
Most key S&P 500 sectors rose, led by financials, telecom and industrials. Energy slumped.
With no major economic releases and no big earnings reports for Tuesday, international developments, and the direction of oil prices, will remain in focus.
London Brent crude traded around $113 a barrel, while U.S. light sweet crude traded below $105.
The dollar rose against a basket of currencies, and the euro fell amid renewed concerns with weaker European economies.
"People are watching oil tick-by-tick," said Joe Saluzzi, co-manager of trading at Themis Trading.
But the equity market, Saluzzi said, is largely driven by the Federal Reserve's $600 billion in bond purchases, and high-frequency traders, who are responsible for some of the big swings seen over the last few weeks. "That’s what keeps the market locked in its range," Saluzzi said.
Also, Saluzzi said, traders who have been burned by betting stocks will fall—or "shorting" the market—are acting more defensively, which is lending support to stocks.
"If they do short, they cover right away," he said.
In the Middle East, the head of the National Libyan Council, the rebel group, offered not to pursue Muammar Gaddafi if he resigns in the next 72 hours, according to Reuters.
Bank stocks led Tuesday's rally, with Bank of America among the leading gainers as its chief executive told investors the bank will cut costs to boost profits, as it continues to address mortgage losses. CEO Brian Moynihan also reiterated the bank's plans to increase its dividend in the second half of the year.
The news gave short-term traders as well as long-term investors a reason to buy the bank's stock, which has been trading at depressed levels, said Scott Redler, chief strategic officer at T3Live.com, who believes the stock could reach as high as $17 or $18 a share this year.
"People want to buy Bank of America," Redler said. "They see it as a play for an improving economy."
Redler also noted that if the S&P 500 is able to get beyond 1,330 or 1,332 in today's move, it "could take us back to the highs of two-and-a-half weeks ago, or obviously higher."
Transportation companies led industrials higher, including Southwest Airlines , Ryder , and Expeditor's International , as an easing in oil prices brought relief to investors. The Dow Jones Transportation Index rose nearly 2 percent.
McDonald's fell despite reporting a 3.9 percent gain in global growthin restaurants open at least 13 months on Tuesday.
And Urban Outfitters sank after the retailer delivered unexpectedly weak profits. Citigroup cut Urban Outfitters' price target to $34 a share from $38, while Wall Street Strategies cut the retailer's rating to "sell" from "hold."
Also, a federal judge extended a temporary order preventing courts in Ecuador from collecting an $18 billion judgment against Chevron .
Boeing rose after news the airline manufacturer signed deals valued at about $10 billion with two Chinese airlines for 2,000 planes over the next 5 years.
Shares of Sprint Nextel spiked amid rumors that Deutsche Telekom plans to sell its T-Mobile USA unit in exchange for a major stake in Spring, according to Bloomberg, citing sources. CNBC reported the two sides were far apart in price a few weeks ago and that nothing seems imminent.
Among tech stocks, Ciena fell for a second day after a disappointing earnings release on Monday, and despite two firms raising their prices targets for the communications equipment company.
Bed, Bath & Beyond slumped after Oppenheimer downgraded the home goods retailer to "perform" from "outperform," and cut its price target to $51 a share from $54, citing the effects of rising cotton prices on profits.
In economic news, the monthly "optimism index" from the National Federation of Independent Business reported its fourth monthly gain on Tuesday. The index, at 94.5, remains below 100, which was the average level for 30 years before the recent recession.
The Treasury will auction $32 billion in three-year notes on Wednesday at about 1 p.m.
Treasury Secretary Timothy Geithner will visit Germany before a European Union summit on rescuing cash-strapped European countries.
On the Calendar:
TUESDAY: 3-year Treasury note auction, BofA investor conference, Nvidia analyst meeting.
WEDNESDAY: Mortgage applications, wholesale trade, oil inventories, 10-year Treasury note auction, BofA/ML consumer conf., Citi 2011 financial services conference, anniversary of S&P 500 closing low (2009); earnings before-the-bell from American Eagle Outfitters and after-the-bell from H&R Block.
THURSDAY: BoE announcement, international trade, jobless claims, quarterly services survey, 30-year Treasury bond auction, Treasury budget, money supply, Nasdaq peak anniversary; Earnings before-the-bell from Smithfield Foods and after-the-bell from National Semiconductor.
FRIDAY: Retail sales, consumer sentiment, business inventories, S&P index rebalancing info due, Apple's iPad 2 ships; earnings before-the-bell from Ann Taylor.
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