The three major USA indexes all posted their biggest one-day percentage gains since March 2009, in the first day of trading following the Christmas holiday, when the market was closed. The Dow has dropped 1 percent or more in eight of the 17 trading sessions.
Financial markets in Australia, Hong Kong were closed for a public holiday, along with bourses in London, Paris and Frankfurt.
The Nasdaq is up 221.36 points, or 3.5 percent. Brent crude, used to price worldwide oils, gained 8 per cent to US$54.47 a barrel in London. Among big retailers, Amazon rose 9.4 percent, Kohl's 10.3 percent and Nordstrom 5.8 percent.
The S&P is now down 15.8 percent since its all-time high on September 20.
The S&P ended Monday 19.8 percent below its all-time closing high, with roughly three-fourths of its stocks already in a bear market. Goldman Sachs declined 1.9 per cent to $159.82 as the yield on the 10-year Treasury fell to 2.76 per cent from 2.79 per cent late Wednesday. The S&P 500 was down 20.06 percent from an intraday record high set on September 21 before Wednesday's sharp rebound.
The S&P 500 is down 205.91 points, or 7.7 percent.
The Dow Jones gained 5 percent or 1,086 points to 22,878.
White House economic adviser Kevin Hassett tried to bring some calm to the markets earlier Wednesday when he assured reporters that Federal Reserve Chairman Jerome H. Powell's job is "100 percent safe".
His reassurance comes two days after Mr Trump tweeted that the Fed, by maintaining its interest-rate-hiking cycle, is the United States economy's "only problem".
Peter Cardillo, chief market economist at Spartan Capital Securities: "With the end of the quarter, we could get a bounce in the next few days", but "the problem is [President Donald] Trump continues to create a lot of uncertainty".
The partial government shutdown that began over the weekend has weighed on the market.
A Mastercard report that sales during the USA holiday shopping season rose 5.1pc to over $850bn in 2018, the strongest in the past six years, helped stocks, as did the higher crude prices.
Among retailers, Macy's gained 4.3 percent and Amazon.com rose 4.3 percent.
Benchmark U.S. crude climbed 8.7 percent to settle at $46.22 a barrel in NY. "Oil prices have just moved quite markedly". Brent crude, used to price global oils, was down 2.6 percent to $53.34 a barrel in London.
The slide in USA markets followed a sell-off in major indexes in Europe.
The dollar fell to 110.53 yen from 111.36 yen on Wednesday. But despite the surge on December 26, it remained on pace for its biggest monthly percentage drop since February 2009, during the throes of the financial crisis. The euro weakened to $1.1351 from $1.1404.
In Asian markets, the Nikkei 225 index rebounded 3.9 percent, while South Korea's Kospi was little changed. Copper fell 1.2 percent to $2.67 a pound.