The Dow rose 273 points to 10,172. All the major indexes climbed more than 2.5 percent. Falling Treasury prices pushed interest rates higher as demand for safe investments eased.
Energy stocks led the market higher after they slid in Wednesday's late trading on concerns that BP would be forced to cut its dividend because of the Gulf of Mexico oil spill. BP rose 12.3 percent from a 14-year low, while Anadarko Petroleum Corp., which has a minority stake in the rig that caused the spill, rose 12.4 percent.
Most bank stocks rose but Goldman Sachs Group Inc. fell 2.2 percent to its lowest level in a year following news reports that it was target of another investigation by the Securities and Exchange Commission. The SEC has already filed civil fraud charges against the company.
Investors have pounded stocks for more than a month because of concerns that Europe's sovereign debt crisis would slow a rebound worldwide. Thursday's advance was the latest swing in market that has been volatile for weeks, including three late-day slides in the past four days. Some of the advance could be coming from what's known as "short-covering." That's when traders are forced to buy stock after having earlier sold borrowed shares in a bet that the market would fall. The moves can add to the market's climb.
Markets around the world rose after China said exports rose 48.5 percent in May, while imports jumped 48.3 percent. The increase in trade provides some relief to fears that debt problems in Europe would halt a global economic recovery. The 27-nation European Union is China's largest trading partner. China has said it wanted to cool its economy to keep it from getting overheated and forming speculative bubbles. Traders had grown concerned that China would inadvertently slow growth too much and hurt a global rebound.
"China so far has been able to pull this off," said John Apruzzese, partner and equity portfolio manager at Evercore Wealth Management in New York. "There's more focus on Europe but I think it's more about China."
The Dow rose 273.28, or 2.8 percent, to 10,172.53. It was the Dow's first close above 10,000 this week and its biggest gain since May 27 when it climbed nearly 285 points after China said it didn't plan to cut its holdings of European government bonds.
The Standard & Poor's 500 index rose 31.15, or 3 percent, to 1,086.84, while the Nasdaq composite index rose 59.86, or 2.8 percent, to 2,218.71.
Brian Lazorishak, portfolio manager at Chase Investment Council in Charlottesville, Va., said he wants to see the market at least hold its gains for a few days before he considers Thursday's advance as more than a blip.
"We've all become a little gun-shy," he said.
The yield on the benchmark 10-year Treasury note, which moves opposite its price, rose to 3.33 percent from 3.18 percent late Wednesday.
The euro, used by 16 countries in Europe, rose to $1.2125. The currency has become an indicator of investor confidence in Europe's economy. It has also influenced stock markets in recent weeks because of concerns that rising debt in countries like Greece, Spain and Portugal would upend the global recovery.
While investors worry about how Europe's debt problems could hurt the rest of the world, there are also concerns about the job market in the U.S. An unemployment rate of 9.7 percent remains one of the biggest obstacles to a strong domestic rebound.
The Labor Department said new claims for unemployment fell by 3,000 to a seasonally adjusted 456,000. While that figure fell short of economists' forecast, investors were heartened by figures showing total claims last week dropped by the largest amount in almost a year. Total unemployment benefit rolls fell by 255,000 to 4.5 million.
On its face, the drop is good news but there it could also indicate that people have run out of their state benefits and are moving to longer-term federal benefits. Still, the drop in total claims provides some hope that laid-off workers are starting to find jobs. It was welcome relief after the Labor Department said last week that private employers slowed their hiring in May to the lowest level since January.
Crude oil rose $1.10 to $75.48 per barrel on the New York Mercantile Exchange. Gold fell.
Among energy stocks, BP PLC rose $3.58, or 12.3 percent, to $32.78, while Anadarko rose $4.32, or 12.4 percent, to $39.15.
Goldman fell $3.03, or 2.2 percent, to $133.77. It traded as low as $131.30, below a previous 12-month low of $134.20.
About 2,700 stocks rose on the New York Stock Exchange, while only about 375 fell. Volume came to 1.3 billion shares, compared with 1.7 billion Wednesday.
The Russell 2000 index of smaller companies rose 21.50, or 3.5 percent, to 639.79.
Britain's FTSE 100 rose 0.9 percent, Germany's DAX index rose 1.2 percent, and France's CAC-40 rose 2 percent. Japan's Nikkei stock average rose 1.1 percent.