NEW YORK — Wall Street rallied back from a sharp, early slump on Monday to notch modest gains after the Federal Reserve unveiled its latest push to prop up the economy.

The S&P 500 climbed 0.8% in the latest day of big swings for global markets, as a remarkable, weekslong rally showed some cracks. Worries are rising that additional waves of coronavirus infections could derail the swift economic recovery that Wall Street just a week ago had seemed so sure was on the way.

When trading began in New York, those worries seemed set to drag the U.S. stock market to a loss following sharp declines in Asia and more modest ones in Europe. The S&P 500 quickly fell 2.5%, with stocks that most desperately need the economy to reopen hit particularly hard.

But some investors took advantage of the nervousness and bought stocks, which helped trim the S&P 500’s losses as the day progressed, before it popped decisively higher after the Fed announced in the afternoon it will buy individual corporate bonds. The purchases will be part of its previously announced program to keep lending markets running smoothly, which allows big employers to get access to cash.

They’re also the latest reminder that the Fed is doing everything it can to help support markets, analysts said. Central banks have repeatedly come to the economy’s rescue over the years, and it was huge, unprecedented moves by the Fed earlier this year that helped put a halt to the S&P 500’s nearly 34% sell-off on worries about the recession coming out of the coronavirus pandemic.

The S&P 500 rose 25.28 points to finish at 3,066.59, which is 9.4% below its record set in February.

The Dow Jones Industrial Average gained 157.62 points, or 0.6%, to finish at 25,763.16 after earlier being down as many as 762 points. The Nasdaq composite added 137.21, or 1.4%, to 9,726.02.

“Volatility is here to stay, at least for a little while,” said Jason Pride, chief investment officer of private wealth at Glenmede. “Nobody in the financial industry has a good way to forecast this.”

Case numbers are still growing in states across the country and nations around the world. Governments are relaxing lockdowns in hopes of nursing their devastated economies back to life, but without a vaccine, the reopenings could bring on further waves of COVID-19 deaths.

China is reporting a new outbreak in Beijing, one that appears to be the biggest since it largely stopped its spread at home more than two months ago. In New York, the governor is upset that big groups of people are packing together outside bars and restaurants without face masks, and he threatened to reinstate closings in areas where local governments fail to enforce the rules.

That’s the biggest worry for markets: If infections swamp the world, governments could bring back the orders for people to stay at home and for businesses to shut down that sent the economy into its worst recession in decades. Even if that doesn’t happen, rolling waves of outbreaks could frighten businesses and consumers enough to keep them from spending and investing, which would itself hinder the economy.

It was just a week ago that investors seemed ebullient about expectations for a coming economic recovery. The hopes got a shot of adrenaline earlier this month when a report showed that U.S. employers added jobs to their payrolls in May, a big surprise when economists were expecting to see millions more jobs lost. That raised expectations that the economy could climb out of its hole nearly as quickly as it plunged into it.

That optimism sent the stock market on a second leg of its rally, which began in March after the Federal Reserve and Congress promised unprecedented amounts of aid to support the economy. Besides its corporate bond buying program, the Fed has also cut interest rates back to nearly zero and expects to keep them there through 2022. Its chair, Jerome Powell, may offer more details about the Fed’s outlook in scheduled testimony before Congress this week.

All through its torrid rally, though, many professional investors were warning that the market’s gains may have been overdone considering how long and uncertain the economic recovery looked to be. The S&P 500 climbed back to within 4.5% of its record high last week.

Some of the rally was likely driven by a big influx of individual investors into the market. Brokerages reported big increases in client numbers and trading earlier this year, and stocks popular with individual investors have returned 61% since the market hit a bottom on March 23, according to Goldman Sachs. That’s much more than the 45% rise for stocks popular with hedge funds and traditional mutual funds.

The yield on the 10-year Treasury note rose to 0.71% from 0.69% late Friday. It tends to rise and fall with investors’ expectations for the economy and inflation, and it had been above 0.90% earlier this month.

In Asia, South Korea’s Kospi dropped 4.8%, Japan’s Nikkei 225 lost 3.5% and the Hang Seng in Hong Kong fell 2.2%. In Europe, France’s CAC 40 slipped 0.5%, Germany’s DAX lost 0.3% and the FTSE 100 in London dipped 0.7%.