Fears that the global economy could be slipping back toward recession sent markets plummeting Thursday, with economic and financial problems around the world fueling a vicious cycle that risks spiraling beyond the control of governments.

On both sides of the Atlantic, economic vital signs are rapidly deteriorating. The U.S. recovery is stalling, and Europe’s debt crisis is threatening to strike Spain and Italy, which have two of the continent’s largest economies.

In the United States, the Dow Jones Industrial Average dropped 512 points Thursday, or 4.3 percent, to close at 11,383. In early trading today in Asia, Japan’s benchmark Nikkei 225 stock average was down more than 3 percent and Hong Kong’s Hang Seng shed 4 percent.

Investors are increasingly afraid that the world’s leading governments, weighed down by debt and wounded by the last economic downturn, may not have the wherewithal to keep the emerging crisis in check.

A dangerous dynamic is taking hold in which the spreading debt troubles in Europe create new risks for the United States, while the chance of another U.S. recession makes the European fiscal crisis even worse. And these perils come as China and other rising economic powers are trying to slow their economies to combat inflation.

Virtually every asset that investors considered risky was in steep decline. U.S. stocks were down 4.8 percent, as measured by the Standard & Poor’s 500 index, and there were similar drops in foreign stocks, oil prices and the debt of financially troubled nations such as Spain and Italy. Prices soared on anything viewed as reliable, including bonds issued by the United States — still considered the best bet if the global economy melts down.

Investors have grown so fearful that they are essentially paying the U.S. government to take their money.

And in a sign of the volatile financial times, Bank of New York Mellon said it will charge depositors of large amounts for the privilege — a 0.13 percent fee on cash deposits of more than $50 million. Large institutions have been avoiding the short-term lending markets where they normally park cash, instead putting it in bank accounts — a practice that banks wish to dissuade because they already have more deposits than they think they can profitably lend out.

The world’s central bankers took a series of actions to address the turmoil in the markets. The European Central Bank on Thursday resumed buying bonds of European nations that investors have been fleeing, helping prop up the value of Irish and Portuguese debt. The Bank of Japan intervened to try to keep the value of the yen from rising so high that it would undermine an already weak Japanese economy. And on Wednesday, the Swiss National Bank made a similar move, seeking to stem a steep rise in the value of the Swiss franc.

The gyrations on financial markets Thursday are ominously reminiscent of the 2008 financial crisis, with nerve-racking moves in the full range of global investments.

“The United States looks like it’s flirting with recession and Europe looks like it’s hitting a full-scale debt crisis,” said Desmond Lachman, a resident fellow at the American Enterprise Institute. “That is a very dark global picture.”

Part of what’s driving the markets’ swoon is a fear that leading governments are not up to the task of addressing a continued deterioration in the economy.

In the United States, a bitter partisan debate over the federal debt ceiling that concluded just days ago reinforced concerns that Washington will be unable to address the nation’s long-term fiscal problems or any coming economic downturn.

“The whole debate over the debt ceiling sent four negative messages to the markets,” said Ethan Harris, chief North American economist for Bank of America-Merrill Lynch. “That we have a big debt problem, that we can’t fix it because we have a dysfunctional political system, that it’s OK to use the threat of default to achieve political ends, and that there’s no safety net if the economy goes into recession because we’re not going to have any more fiscal stimulus.”

Some U.S. businesses reported in recent weeks that they had delayed hiring and investment decisions because of uncertainty about whether the government would leave the debt ceiling unchanged and thus default. Businesses’ reluctance to spend could be reflected in a key report on the job market, to be released this morning, which will be the latest evidence on whether the U.S. economy is sustaining its recovery.

The Federal Reserve, meanwhile, is planning to hold its regularly scheduled policy meeting Tuesday. But the Fed has already taken extraordinary measures in recent years to boost the economy, including near-zero interest rates for 2½ years and counting, and is unlikely to find any silver bullets.

The Fed is likely to consider modest steps to ease monetary policy, such as promising to keep interest rates low for some set period in the future or delaying plans to reduce its multitrillion-dollar portfolio of bonds. The central bank could even decide at some point to expand its large-scale purchases of bonds — which have the effect of making cheaper money available to businesses and consumers — if the economy starts to slump.

Europe is dealing with a debt crisis that has engulfed some of its largest economies. So far, European nations, particularly Germany and France, have been willing to help bail out smaller countries such as Greece, Portugal and Ireland that have run into trouble. But if investors start to turn on Italy and Spain, charging them unaffordable rates to borrow money, it might be impossible to come up with a rescue package that is large enough.