On Wall Street, IBM (>> International Business Machines Corp.) shares closed down 7.1 percent at $169.10. While IBM's miss limited the Dow's gains, the index turned modestly higher before the end of the U.S. session, while the S&P 500 and Nasdaq advanced.

"The fact that the Dow has been able to get positive with IBM's 13-point decline is pretty significant. It shows the overall strength in the market," said Philip Orlando, chief equity market strategist at Federated Investors in New York. "We're continuing to rebound off of oversold levels," he said.

U.S. corporate earnings season will ramp up this week, with nearly 130 S&P 500 companies scheduled to report. Apple Inc (>> Apple Inc.) posted a better-than-expected 12 percent jump in revenue after Monday's close . Shares in Apple were roughly flat at about $100 in after-hours trade.

European stocks closed lower, meanwhile, after a profit warning from German business software maker SAP (>> SAP SE) hit technology shares.

"It's all about growth at the moment. Cyclicals have been underperforming in recent months ... (and) with respect to SAP, it's a result of the business investment climate," said Mike Ingram, market strategist at BGC Partners.

Japan's Nikkei average <.N225> surged 4 percent, underpinned by news that Japan's $1.2 trillion public pension would likely more than double its allocation to domestic stocks to about 25 percent. The Nikkei's gain on Monday marked its biggest daily rise since June 2013.

MSCI's all-country world index <.MIWD00000PUS>, which tracks shares in 45 nations, was last up 0.74 percent to 399.94, while the FTSEurofirst 300 index <.FTEU3> of top European shares closed down 0.58 percent at 1,272.72.

The Dow Jones industrial average <.DJI> closed up 0.12 percent, at 16,399.67, while the S&P 500 <.SPX> ended up 0.91 percent, at 1,904.01. The Nasdaq Composite <.IXIC> ended up 1.35 percent, at 4,316.07.

Benchmark 10-year U.S. Treasury notes were last up just 1/32 in price to yield 2.19 percent. The U.S. dollar index <.DXY>, which tracks the greenback versus a basket of six currencies, fell 0.13 percent, to 85.001.

Brent crude resumed its decline on nagging concerns about abundant supply and sluggish demand and fell as low as $84.41. It was last down $0.85, or 0.99 percent, at $85.31 a barrel. U.S. crude settled down 4 cents at $82.71 a barrel.

(Additional reporting by Atul Prakash in London, Alistair Smout in Edinburgh, and Chuck Mikolajczak and Richard Leong in New York; Editing by Meredith Mazzilli, James Dalgleish and Andrew Hay)

By Sam Forgione

Stocks treated in this article : International Business Machines Corp., Apple Inc., SAP SE