U.S. and European stock markets plummeted again Wednesday as the debt crisis rocking a handful of smaller European nations threatened to engulf the continent’s biggest economies, France and Germany.

Major markets on both sides of the Atlantic declined by more than 4 percent, with investors dumping financial stocks in particular amid signs that the debt crisis on the periphery of Europe is rapidly becoming a banking crisis at its core.

The Dow Jones industrial average fell 520 points, or 4.6 percent, to 10,720, while the Standard & Poor’s 500 dropped 52 points, or 4.4 percent, to 1,121. The declines erased the major gains made Tuesday and dashed hopes that the markets were starting to rebound from their recent lows.

With fears of a fresh financial crisis on the rise, President Obama met with Federal Reserve Chairman Ben S. Bernanke and Treasury Secretary Timothy F. Geithner at the White House to review the developments. A White House spokesman said that Obama is not overly concerned with day-to-day gyrations in the market and that he plans to meet with business executives to discuss the economy.

In France, President Nicolas Sarkozy raced back to Paris from his vacation on the Riviera for an emergency meeting of his economic advisers amid rumors in financial circles that the country could soon lose its top-notch credit rating if it is forced to bail out its banks.

On many global markets, trepidation about the health of Europe’s financial firms overtook concerns about the slow pace of the U.S. economic recovery and the stunning downgrade last week of the nation’s credit rating by Standard & Poor’s.

Shares of all the major European banks — including Germany’s Deutsche Bank, France’s BNP Paribas and Britain’s Barclays — fell sharply in trading. Speculators, meanwhile, increased their bets that the firms could collapse, although the odds, as measured by the cost of insurance against a default, remained low.

The steepest decline was at the French firm Societe Generale, one of the world’s largest banks, with $1.6 trillion in assets. The bank was forced to issue a statement denying “all market rumors” about its solvency and announced that it had solid earnings in July and August.

The problem for banks in France and Germany is that they have loaned hundreds of billons of euros to the governments of Spain, Greece, Ireland, Italy and Portugal. These governments are now struggling to avoid defaulting on their obligations.

Although investors have been expressing concern for months about the exposure of French and German banks to the troubled debt of other European countries, this has turned to alarm only in recent days, fueled by a generalized anxiety about the world economy.

If major European banks were to suffer massive losses, that could ripple across the global financial system. Although U.S. banks have limited direct exposure to European government debt, they do extensive business with European financial firms.

“A default or even a serious decline in the value of Italian and Spanish bonds would leave most of the French and German banking systems technically insolvent,” said Robert Shapiro, chairman of Sonecon, an economic consulting firm. “This is a very serious problem. You have a full-on global financial crisis if one of the major European banks goes down.”

On Wednesday, European banks borrowed 50 billion euros, an unusually large sum, from the European Central Bank, giving themselves more cash at a time when private lending between banks is showing new strains.

The rate that banks charge to lend dollars to each other for three months, known as the London Interbank Offered Rate, or Libor, rose to a four-month high of 0.28 percent Wednesday, a sign of heightened concern.

France, which had long been considered safe from Europe’s debt crisis, has faced speculation this week that it could lose its AAA credit rating if the government is forced to spend billions of euros to rescue its banks. France is coming under increased scrutiny from investors because, like the United States, it has a large and growing national debt, caused in part by underfunded social programs for retirees.

After Sarkozy met with his economic advisers, he called for new measures to cut government spending and tax loopholes to reduce the government’s budget deficit. He also declared that “pledges will be kept, whatever the evolution of the economic system.”

France received a boost when the major credit rating firms reaffirmed the country’s AAA rating.

The prognosis for Europe worsened this week because of new indicators showing that the German economy, which has been the continent’s leading engine, could be slowing amid a downturn in Germany’s exports.

The steep market losses occurred even though financial policymakers have had some success in containing the crises in Spain and Italy, the fourth- and fifth-largest economies in Europe, respectively.

Over the weekend, the European Central Bank announced that it would start buying Italian and Spanish bonds in an effort to keep the cost those countries pay to borrow from rocketing to prohibitive levels. Investors continued to respond favorably Wednesday as the yields on those bonds declined for the third straight day.

In the United States, large banks such as Bank of America and Citigroup came under pressure, declining by more than 10 percent in trading.

U.S. stock markets have been dropping for most of the the past two weeks. They took a severe hit Monday, falling the most since the 2008 financial crisis. Markets bounced back Tuesday before giving up those gains — and more — Wednesday. The Dow is down 20 percent from its recent high, while the S&P is down more than 18 percent.

Between July 22 and Monday, about $3 trillion in U.S. market value and $8 trillion globally has been eliminated, according to data compiled by Bloomberg.

Money again gushed into U.S. Treasury bonds, which investors consider safe. The price that the U.S. government must pay to borrow money for a decade fell for the third straight day, down 0.14 percentage point, to 2.1 percent. Just two weeks ago, the same interest rate was 3 percent.

The market’s swoon in part reflects a deepening sense that the U.S. economy is weaker than it seemed just a month ago and is at risk of dipping back into recession.

“Capital markets are repricing to reflect the economy that we have, as opposed to the economy that everyone hopes we’re going to get,” said Steve Blitz, senior economist at ITG Investment Research.

The Federal Reserve said Tuesday that it expected the economy to remain sluggish for an extended time and announced that short-term interest rates would be kept at “extremely low” levels at least through mid-2013. But the Fed did not announce more aggressive measures to boost the economy.

At Treasury, Geithner and top advisers have been in close communication with finance ministers and central bank officials in Europe, as well as U.S. banking regulators, a department official said.

And at the White House meeting, Obama and top economic policymakers discussed the prospects for the recovery and jobs, according to an official statement.They also took up fiscal issues, including the federal deficit, and reviewed the situation in Europe. The session was the third time Obama has met with Bernanke this year.

At his daily briefing, White House press secretary Jay Carney said the president is focused on the economy and has been in touch with foreign leaders, including speaking about the economy to British Prime Minister David Cameron on Wednesday.

“The president’s focus is not on the daily ups and downs of the market,” Carney said.