Despite the rally in stocks, U.S. Treasury yields were little changed.

European shares pulled up from Monday's 22-month lows <.STOXX>, partly on expectations that the reporting season will deliver double-digit earnings growth. A rebound in Italian assets helped battered equities find firmer ground.

On Wall Street, tech shares led the way a day after a decline in Apple weighed on the Nasdaq, while the healthcare sector rose after earnings reports from Johnson & Johnson and UnitedHealth Group.

"A couple of inputs that caused a sell-off in the last two weeks, such as rising interest rates, higher oil prices and the dollar, have calmed down to rational levels," said Art Hogan, chief market strategist at B. Riley FBR in New York.

"The market may be able to positively respond to that as we work our way through the earnings season."

Willie Delwiche, investment strategist at Baird in Milwaukee, said Tuesday's gains were the result of sharp selling over the past weeks.

"The degree of the move is a function of the moves we have seen already this month more than anything else," he said.

The Dow Jones Industrial Average rose 547.87 points, or 2.17 percent, to 25,798.42, the S&P 500 gained 59.13 points, or 2.15 percent, to 2,809.92 and the Nasdaq Composite added 214.75 points, or 2.89 percent, to 7,645.49.

The pan-European FTSEurofirst 300 index <.FTEU3> rose 1.41 percent and MSCI's gauge of stocks across the globe <.MIWD00000PUS> shed 0.45 percent.

Emerging market stocks lost 0.86 percent. MSCI's broadest index of Asia-Pacific shares outside Japan <.MIAPJ0000PUS> closed 1.11 percent lower.

OIL WOBBLES

Crude futures rose in choppy trading as expectations of higher U.S. shale output and inventories were more than offset by worries over looming U.S. sanctions on Iran and growing tensions with top oil producer Saudi Arabia.

U.S. Senator Lindsey Graham accused Saudi Crown Prince Mohammed bin Salman of ordering the murder of Saudi journalist Jamal Khashoggi and said the prince was jeopardizing relations with the United States.

U.S. crude rose 0.07 percent to $71.83 per barrel and Brent was last at $81.32, up 0.67 percent on the day.

Sterling rose against the dollar after data showed basic wages of workers in Britain rose at their fastest pace in nearly a decade. The British currency was last trading at $1.3187, up 0.28 percent on the day.

Meanwhile, a survey showed German investor morale darkened more than expected in October.

The euro fell 0.03 percent to $1.1573, while the Japanese yen weakened 0.47 percent versus the greenback at 112.30 per dollar. The dollar index <.DXY> rose 0.01 percent.

Investors waited for Washington's view on China in the U.S. Treasury's semiannual currency report due this week, after media reports last week that it has not labelled Beijing a currency manipulator.

Benchmark 10-year Treasury notes last rose 1/32 in price to yield 3.1614 percent, versus 3.163 percent late on Monday.

The 30-year bond last rose 6/32 in price to yield 3.3312 percent, from 3.341 percent late on Monday.

"Following the extraordinary volatility in both stocks and bonds, we are seeing a bit of a calming here as traders are looking for new ranges," said John Canavan, market strategist at Stone & McCarthy Research Associates in New York.

Investors scaled back bearish bets on longer-dated U.S. government debt this week, suggesting less selling pressure on Treasuries, according to a survey released by J.P. Morgan Securities on Tuesday.

(Reporting by Rodrigo Campos, Karen Brettell, Devika Krishna Kumar Lewis Krauskopf and Richard Leong in New York; additional reporting by Medha Singh in Bengaluru; Editing by Nick Zieminski and Dan Grebler)

By Rodrigo Campos