The huge gains clawed back some of the ground lost last week in a massive sell-off that gave stocks their worst stretch since the financial crisis of 2008.
Technology companies led the broad gains, which gave the Dow its biggest-ever point gain and biggest percentage increase since March 2009. The S&P 500 index jumped 4.6%, its best day since December 2018.
European benchmarks were mostly higher, and Asian markets rose broadly.
Bond prices fell, pushing yields higher after having touched another record low earlier in the day. The yield on the 10-year Treasury note rose to 1.15% from 1.12% late Friday.
The virus outbreak that began in central China has been shutting down industrial centers, emptying shops and severely crimping travel all over the world. More companies are warning investors that their finances will take a hit because of disruptions to supply chains and sales.
Amid the worsening outlook, investors are increasingly anticipating that the Federal Reserve and other major central banks around the world will lower interest rates or take other steps to shield the global economy from the effects of the outbreak.
"Investors have convinced themselves that global central banks will likely be even more accommodative in order to short-circuit any psychological damage, " said Sam Stovall, chief investment strategist at CFRA.
Bill Nelson, chief economist at the Bank Policy Institute and a former Fed economist, said the Fed and other major central banks, possibly including China's, could announce coordinated rate cuts by Wednesday morning. The cut would at least be a half-point and perhaps even three-quarters, he said.
"The only way to get a positive market reaction is to deliver more than expected," he said.
The International Monetary Fund and World Bank announced simultaneously Monday that they are ready to help countries affected by the coronavirus through their emergency lending programs and other tools.
"We will use our available instruments to the fullest extent possible," the IMF managing director, Kristalina Georgieva, and World Bank President David Malpass said in a joint statement. "International cooperation is essential."
And Christine Lagarde, the head of the European Central Bank, said Monday that Europe's top monetary authority is ready to take "appropriate and targeted measures" if necessary to support the economy against the headwinds from the new coronavirus.
The statements echoed similar promises to act if necessary from the Federal Reserve on Friday and the Bank of Japan over the weekend. Traders have priced in a 100% probability that the Fed will cut rates by a half-percentage point during or before its March meeting.
One encouraging sign to traders is that the finance ministers and central bank leaders of the Group of Seven major industrial countries will hold a conference call on Tuesday to discuss an economic response to the viral outbreak.
U.S. Treasury Secretary Steven Mnuchin and Federal Reserve Chairman Jerome Powell will lead the call. The group includes Japan, Germany, Britain, and France, among others. The G-7 often issues statements pledging cooperation amid global economic turbulence.
There were signs that the economic impact was continuing to mount. A measure of China's manufacturing output plunged last month to its lowest level on record, as the viral outbreak closed factories and disrupted supply chains.
And the Organization for Economic Development, a research organization made up of mostly advanced economies, said Monday that the viral outbreak "presents the global economy with its greatest danger since the financial crisis" in 2008.
The OECD cut its world growth forecast and said that even if there are only limited outbreaks outside China, the global economy will grow just 2.4% this year, the weakest since the crisis. That forecast matches several private estimates.
If other countries are hit with outbreaks similar to China's, growth could fall as low as 1.5%, the OECD said.
Separately, economists at Goldman Sachs slashed their forecasts for U.S. growth to just 0.9% in the first quarter and to zero for the April-June quarter.
For investors, the great amount of uncertainty over how consumer behavior and spending will be affected has been unsettling.
"It's not a typical economic blow," said Bill Strazzullo of Bell Curve Trading. "What if major cities are on some kind of a lockdown? What will that do to restaurants, entertainment, shopping, travel? It's almost impossible to game this out."
Last week's rout knocked every major index into what market watchers call a "correction," or a fall of 10% or more from a peak. Market watchers have said for months that stocks were overpriced and long overdue for another pullback.
The last time the market had a drop of that size was in late 2018, when the trade war with China was escalating and investors were worried about rising interest rates. With Monday's surge, the S&P 500 is now 8.7% below the record high it reached February 19.
The stock surge notwithstanding, the fact that investors are holding onto Treasurys at near record-low yields shows they are still worried.
"The fear factor is still very high," said Kirk Hartman, president of Wells Fargo Asset Management. "Do you really want to own a 10-year Treasury at 1 percent? I don't think so. I think this is a classic market in crisis."
Shoppers stocking up on everyday goods as fear over the coronavirus' spread hits consumers helped lift shares in household goods companies. Costco jumped 10%. Walmart rose 7.6%. Procter & Gamble gained 5.6%.
Technology and health care stocks accounted for a big share of the gains. Apple climbed 9.3% and Gilead Sciences rose 8.7%. The biotechnology company has been testing one of its drugs as a potential treatment for the coronavirus.
Stimulus hopes helped shore up markets in Asia earlier. The Nikkei 225 index closed 1% higher, while the Shanghai Composite index rose 3.2%.
China has seen most of the 90,000 or so virus cases worldwide. In the United States, authorities have counted at least 80 cases of the virus, six fatal, and concern was driving some to wipe store shelves clean of bottled water, hand sanitizer and other necessities. Both deaths were men with existing health problems who were hospitalized in Washington state.
MARKET ROUNDUP:
The Dow jumped 1,293.96 points, or 5.1%, to 26,703.32. The S&P 500 index gained 136.01 points, or 4.6%, to 3,090.23. The Nasdaq added 384.80 points, or 4.5%, to 8,952.16. The Russell 2000 index of smaller company stocks picked up 42.06 points, or 2.9%, to 1,518.49. Even with Monday's big rally, the major U.S. indexes remain in the red for the year.
Oil prices have also slumped as traders priced in the prospect of lower demand as a result of the virus outbreak. Last week, oil prices tanked by around 15%. On Monday, benchmark U.S. crude rose $1.99, or 4.4%, to settle at $46.75 a barrel. Brent, the international standard, gained $2.23 to close at $51.90.
Wholesale gasoline rose 57 cents to $1.54 per gallon. Heating oil climbed 5 cents to $1.53 per gallon. Natural gas rose 7 cents to $1.76 per 1,000 cubic feet.
Gold rose $28.20 to $1,592.30 per ounce, silver rose 29 cents to $16.68 per ounce and copper rose 5 cents to $2.60 per pound.
The dollar fell to 107.87 Japanese yen from 108.42 yen on Friday. The euro strengthened to $1.1163 from $1.1028.