Updated August 24, 2015 at 5:25 p.m. ET
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■ Stock markets in the United States traded in a volatile session, with the Standard & Poor’s 500-stock index closing down nearly 4 percent.

■ Many investors sought refuge from the upheaval by turning to American and European government bonds.

■ In China, the benchmark Shanghai composite index erased all of the gains it had made this year.

■ In Europe, stocks fell sharply, with the main indexes closing down 5 percent or more.

■ The American and international oil benchmarks have fallen to their lowest point in more than six years.

■ An index that measures market volatility reached levels last seen in 2011 when Americans were worrying about a double-dip recession.

In-Depth

Stock prices around the world bounced around wildly on Monday as investors debated if and when governments are likely to step in to calm the turmoil that has recently spiraled out from China.

The Dow Jones industrial average plunged over 1,000 points immediately after the opening bell on Monday morning before recovering much of those losses and then dropping again nearly 600 points to close at 15,871.28.

Traders confronted a volatile morning at the New York Stock Exchange on Monday.CreditSpencer Platt/Getty Images

That followed a stock market rout in China — immediately named “Black Monday” by local commentators — in which the main Shanghai stock index fell 8.5 percent.

The day’s trading began with questions about whether the Chinese government would make further efforts to support local investors. When Chinese authorities didn’t get involved, the talk on trading floors turned to the Federal Reserve’s current plans to ease up on its stimulus program, and whether that might change in light of the recent tumult.

“Everything is going to be dictated by government policy,” said Kevin Kelly, the chief investment officer of Recon Capital Partners. “Whatever noise is coming from policy makers is going to determine the next couple weeks.”

The conversation about government policy is playing into a broader debate about the global economy’s ability to continue growing without the sort of extraordinary stimulus that has become the norm in recent years.

In the United States, the major indexes had pared back much of their early losses in midday but again resumed their fall.

The S.&P. 500 closed down 3.9 percent, at 1,893.21. The index is off more than 11 percent from its high in May, indicating a so-called correction. The Nasdaq ended Monday down 3.8 percent to 4,526.25.

Investors’ worries over China’s economic slowdown and a souring view of emerging economies have rattled financial markets around the world in recent days, and showed no signs of letting up.

“There was a huge amount of negative sentiment built in this morning,” said Dan Greenhaus, the chief global strategist at BTIG.

Mr. Greenhaus said many investors ended last week hoping that the Chinese government would step in over the weekend to announce some steps to support the markets, but nothing significant was announced, contributing to the pessimism on Monday morning.

The negative sentiment led to the big market drops in early trading Monday morning, with the S.&P. 500 initially down more than 5 percent and the Nasdaq down more than 8 percent. The bounce back from those early lows by midday suggested that at least some investors were convinced that the panic has gone too far.

Ryan Larson, the head stock trader at RBC Global Asset Management, said that after the initial market declines clients were canceling their sell orders and putting in requests to buy stocks. Although some American companies may be hit by the weakness in the emerging markets, recent data has suggested that the American economy is continuing to strengthen.

The shares of Apple were in positive territory for a bit after its chief, Timothy D. Cook, sought to reassure investors that the company’s sales were still strong in China.

Still, few investors were calling an end to the volatility that has shaken markets in recent weeks.

Among the biggest losers in the main indexes were oil stocks like ExxonMobil as crude oil prices traded below $40 a barrel.

The so-called fear index, the Vix, was up on Monday morning to levels last reached in 2011 when Americans were worrying about a double-dip recession.

Investors flocked to the safe haven of Treasury bonds. The demand for bonds pushed the yield on the benchmark 10-year Treasury note briefly to 1.90 percent before it recovered back over the psychologically significant 2 percent mark.

In China, the benchmark Shanghai composite index closed 8.5 percent lower on Monday, erasing all of the gains it had made in an extraordinary run-up this year. And in Europe, stocks fell sharply, with several of the main indexes down by 6 percent or more in late-afternoon trading.

The broad-based sell-off in stocks poses a challenge to the Federal Reserve in the United States. The central bank’s chairwoman, Janet L. Yellen, and her colleagues on the Fed’s policy board have been warning investors for months that the central bank was moving toward the first increase in its main interest rate since it was cut to zero in December 2008.

Many analysts have said that a correction to stock market valuations was overdue after a long bull market. And it is too early to say how the financial market slump will affect the underlying global economy where goods and services are actually produced and consumed.

Many of the world’s central bankers will have a chance later this week to compare notes and discuss whether new policy steps are needed when they gather, along with finance ministers and academics, in Jackson Hole, Wyo., for the Federal Reserve Bank of Kansas City’s annual conference.

“People who had wanted to bottom-feed by buying earlier this morning are all losing money,” said Andy Wong, a Hong Kong stockbroker. “The market trend does not look good, it is all bad news, globally. All the markets are going down, globally; the Chinese stock markets are in free fall today.”

Leung Chung, a 62-year-old retiree and day trader in a T-shirt and with a toothpick in his mouth, looked sourly at the monitors at his local brokerage firm in late morning. “I just purchased some stocks earlier this morning, but have already lost money,” Mr. Leung said. “I am not too concerned as I only bought stocks with solid financial strength.”

The dollar rose against most Asian currencies, with the exception of the yen, which is considered a regional haven.

The euro gained 1.8 percent against the dollar, trading at $1.1585 late afternoon on Monday.

Lee Hardman, a currency analyst at Bank of Tokyo-Mitsubishi UFJ in London, said in a research note that the rising euro and yen were “creating a policy headache for the European Central Bank and Bank of Japan,” as well as for the Fed.

Stronger currencies, he said, would make it harder for central banks to fight deflationary pressures. He noted that long-term forecasts for the eurozone showed inflation beginning to return to the levels that existed before the European Central Bank began its bond-buying program this year.

One big question is whether China’s stock market plunge will make the Chinese economy, the world’s second-largest after that of the United States, even weaker. China’s exports were down 8 percent in July compared with a year earlier, while auto sales were down 7 percent.

But Xu Sitao, the chief China economist in the Beijing office of Deloitte, said in a speech in Hong Kong that the effect on the economy could be muted because equities represent only 7 percent of the overall wealth of urban Chinese households, which continue to rely very heavily on real estate in their holdings.

“The stock market really has a very, very insignificant impact on the Chinese economy,” he said.

Despite this, the market continued to slump. On Monday, the Shanghai index fell to its lowest level this year; it traded as low as 3,191.88 points, a drop of 9 percent from the close on Friday and nearly 40 percent below its peak in June. Mainland shares are only allowed to rise or fall by 10 percent per day before they are suspended from trading. Shares in more than 800 of the nearly 1,100 companies in the Shanghai index fell by the limit.

The plunge in Shanghai came despite an announcement by China’s government on Sunday that the country’s pension funds had been approved for the first time to invest in stocks.

Pension funds can invest as much as 30 percent of their holdings in the stock market, according to the statement by the State Council, China’s cabinet. The main state-run pension fund manages about 3.5 trillion renminbi, or about $550 billion, in retirement savings of ordinary citizens.

Many economists expect the central bank, the People’s Bank of China, to cut the ratio of deposits that banks are required to keep on reserve in a bid to help stem outflows of capital, which rose to a record of $70 billion in July and probably accelerated in the weeks since the renminbi was devalued.

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