Japan's Nikkei 225 index jumped 5.3%, while Hong Kong added 3% and Sydney climbed 3.6%. Markets across Asia were all up more than 2%.

The Dow burst 11.4% higher, while the more closely followed S&P 500 index leaped 9.4% as a wave of buying around the world interrupted what has been a brutal month of nearly nonstop selling. Investors released some frustration that had pent up over days of watching the U.S. Senate stalemate over the crucial rescue package.

Despite the gains, investors were far from saying markets have hit bottom. Rallies nearly as big as this have punctuated the last few weeks, and none lasted more than a day. Economists and investors alike are still expecting to see some dire economic numbers in the days and weeks ahead.

"Today was a good day, but we would not necessarily see this as turnaround time," said Adam Taback, chief investment officer for Wells Fargo Private Bank.

Both Democrats and Republicans said Tuesday they're close to agreeing on a massive economic rescue package, which will include payments to U.S. households and aid for small businesses and the travel industry, among other things. A vote in the Senate could come later Tuesday or Wednesday.

Investors were imploring Congress to act, particularly as the Federal Reserve has done nearly all it can to sustain markets, including its latest round of extraordinary aid launched Monday.

"It's sort of like, keep the patient alive in the emergency room so you can provide some treatment options," said Katie Nixon, chief investment officer at Northern Trust Wealth Management.

The Dow rose 2,112.98 points, its biggest point gain in history, to 20,704.91. The S&P 500, which is much more important to most 401(k) accounts, rose 209.93, or 9.4%, to 2,447.33 for its third-biggest percentage gain since World War II. The Nasdaq composite jumped 557.18 points, or 8.1%, to 7,417.86.

In Asia early Wednesday, Tokyo's Nikkei was at 19,053.40, while the Hang Seng rose to 23,374.57. South Korea's Kospi gained 4.2% to 1,678.13 and the S&P/ASX 200 picked up 3.6% to 4,906.10. Taiwan's benchmark jumped 4.4%.

U.S. crude oil gained 88 cents to $24.89 per barrel in electronic trading on the New York Mercantile Exchange. Brent crude, the international pricing standard, added 91 cents to $30.65 per barrel.

In currency trading, the U.S. dollar was at 110.90 Japanese yen, down from 111.22 yen late Tuesday. The euro rose to $1.0803 from $1.0790.

Earlier share rebounds have evaporated. Since stocks began selling off on Feb. 20, the S&P 500 has had six days where it's risen, and all but one of them were big gains of more than 4%. Afterward, stocks fell an average of 5% the next day.

"One of the things to be careful about is thinking this will be the panacea or that this fiscal response will be sufficient," said Eric Freedman, chief investment officer at U.S. Bank Wealth Management.

Ultimately, investors say they need to see the number of new infections peak before markets can find a floor. The increasing spread is forcing companies to park airplanes, shut hotels and close restaurants to dine-in customers.

President Donald Trump said Tuesday during a Fox News virtual town hall that he hopes to "open up " the economy by Easter. Analysts said the pronouncement wasn't a contributor to the day's huge rally, which was mostly due to the stimulus hopes.

For most people, the coronavirus causes only mild or moderate symptoms, such as fever and cough. Those with mild illness recover in about two weeks. Severe illness including pneumonia can occur, especially in the elderly and people with existing health problems. Recovery could take six weeks in such cases.

Economists are topping each other's dire forecasts for how much the economy will shrink this spring due to the closures of businesses, and a growing number say a recession seems inevitable.

Some of the market's areas hardest hit by the closures, though, led the way higher Tuesday as expectations rose for incoming aid from the U.S. government.

Norwegian Cruise Lines, MGM Resorts and American Airlines Group were all up at least 33%. Energy companies and banks were also strong, though all remain well below where they were a month ago.

Governments and central banks in other countries around the world are unveiling unprecedented levels of support for their economies in an attempt to limit the scale of the upcoming virus-related slump. Germany, a bastion of budgetary discipline, also approved a big fiscal boost.

The gains came even as the first reports arrived showing how badly the outbreak is hitting the global economy. In the United States, a preliminary reading on business activity in March showed the steepest contraction on record, going back to 2009. Reports were also gloomy for Europe.

"Everyone was prepared for a set of shockers, and that is precisely what we got, but they are not a surprise," said Chris Beauchamp, chief market analyst at IG. "It is at times like this that the market's propensity to look forward is demonstrated most effectively."

More gloomy data is nearly assuredly on the way. On Thursday, economists expect a report to show the number of Americans applying for jobless claims easily set a record last week. Some say the number could be way beyond 1 million, amid a wave of layoffs, topping the prior record of 695,000 set in 1982.

Helping to lift sentiment in markets was news from China that it is preparing to lift the lockdown in Wuhan, the epicenter of the outbreak, and from Italy reporting a reduction in the number of new cases and coronavirus-related deaths.

"It's still early days, of course — perhaps investors can start to envisage life beyond the coronavirus," said Craig Erlam, senior market analyst at OANDA Europe. "That could make stocks look a little more attractive, although anyone jumping back in now will need to have nerves of steel."

Despite Tuesday's big gains, it's no time to get complacent, said Wells Fargo's Taback.

"We would caution that the danger is not all behind us at this point," he said. "We still have not seen numbers that give us an indication of just how bad things are."