Jeff Kleintop, chief market strategist at LPL Financial, said the market appeared to be turning on rumors and speculation. But the chatter was enough to convince some traders that the worst was over for now.

As of Monday, worries about Greece and Spain had pulled the Standard & Poor's 500 index down nearly 10 percent from its peak in early April. "The next 10 percent move is not down, it's up," Kleintop said.

LPL has started to pull back on bets against the S&P 500 and the euro. "We've decided it's time to declare victory," Kleintop said.

A speech by a Federal Reserve official also added to speculation that the Fed may take more steps to bolster the U.S. economic recovery. Dennis Lockhart, president of the Fed's Atlanta regional bank, says weak job growth over the past two months highlighted the "halting and tenuous" recovery. If the trend continues, "further monetary actions to support the recovery will certainly need to be considered," he said.

Federal Reserve Chairman Ben Bernanke will likely be asked about more actions to help the economy when he testifies before a congressional committee on Thursday.

Companies whose stocks have been clobbered the most over the past month had the best gains. Homebuilders rallied, helped by a strong earnings report from Hovnanian Enterprises and rising applications for new mortgages. Hovnanian's CEO said he sees signs that the housing industry may be entering the early stages of recovery. The Mortgage Bankers Association reported that applications for mortgages rose 1.3 percent last week, largely a result of more people trying to refinance their existing loans.

Hovnanian leapt 18 percent. PulteGroup Inc. surged 7 percent and Lennar Corp. 4 percent.

The gains were spread across the market. Only 11 companies in the S&P 500 dropped, and every industry group in the index rose, led by energy and financial companies. Roughly seven stocks rose for every one that fell on the New York Stock Exchange.

Jim Russell, chief equity strategist at U.S. Bank Wealth Management in Cincinnati, Ohio, said it's natural for the market to have a strong day after an extended beat-down. On such days, it's usually the companies that were hit the hardest that fare best.

"In market language, it's called a technical bounce," he said. "There's no bad news today, so the market goes up. Frankly, it's that simple."

U.S. markets followed major European indexes higher. Indexes rose 2.4 percent in the U.K. and France. Borrowing costs eased for Spain, another positive sign.

In other trading, the Standard & Poor's 500 rose 29.63 points to 1,315.13. The Nasdaq composite rose 66.61 points to 2,844.72.

A Federal Reserve survey showed growth across the country. Hiring was steady, according to the Fed's "Beige Book." That's in marked contrast to the government's monthly jobs report, which said employers added the fewest jobs in a year last month.

The dollar dipped and Treasury yields rose as investors moved money out of defensive investments. The yield on the benchmark rose to 1.64 percent from 1.57 percent late Tuesday.

Among stocks making big moves:

— Morgan Stanley jumped $1.08, 8 percent, to $13.94 amid reports that the Blackstone Group and other private equity firms may try to buy a stake in the bank's commodities business.

— UnitedHealth Group gained $1.66, 3 percent, to $57.70 after the health insurer said it will raise its quarterly dividend from 16 cents to 21 cents per share . The board also approved a plan to buy back stock.

— Tempur-Pedic International plunged $21.28, 49 percent, to $22.39. The mattress maker said it expects quarterly profits to fall by half compared to last year. Tempur-Pedic blamed its competitors' aggressive marketing campaigns and promotions for hurting its sales.