On Friday, the Dow and S&P closed up more than 1 percent for their biggest reversal in four years.
Analysts attributed the turnaround mostly to technical factors. Stocks initially sold off sharply Friday after a weaker-than-expected September nonfarm payrolls report. Few analysts found any positives from the data, which showed creation of 142,000 jobs and revised August and July figures lower.
Unemployment held at 5.1 percent, according to the Labor Department. The participation rate plunged to 62.4 percent, meaning the Fed may not be able to raise rates this year, which would remove some uncertainty for investors.
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In Monday's earnings news, The Container Store was due to post results after the bell.
Third-quarter earnings season kicks off later in the week with PepsiCo, Alcoa and a few other companies reporting. Earnings are expected to decline 3.9 percent for the S&P 500, according to Thomson Reuters.
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In Europe, stocks closed more than 2.5 percent higher after the weaker-than-expected U.S. jobs report dampened expectations of a rate hike this year. Glencore surged to close up more than 16 percent.
Japan's Nikkei and Hong Kong's Hang Seng both rose more than 1.5 percent to 2-week highs. Mainland Chinese markets are closed until Wednesday for the National Day holidays.
"Global equity markets are rallying this morning following Friday's bullish reaction to the jobs report in the U.S. We view last week's price action as characteristic of a bullish shakeout, as per our latest Global Technical Strategy, and would be adding exposure in anticipation of a seasonal fourth-quarter rally," Katie Stockton, chief technical strategist at BTIG, said in a note.
In U.S. economic news, ISM non-manufacturing came in at 56.9 for September, below August's 59 read and expectations of 57.5. The ISM manufacturing report last week showed softness in the manufacturing sector.
"Bottom line, the U.S. service sector certainly moderated in September but an index at 56.9 is still a healthy level of growth for this most crucial and largest part of the U.S. economy. Manufacturing is certainly challenged but the more domestic-dependent services side has been able to weather the global economic slowdown much better," Peter Boockvar, chief market analyst at The Lindsey Group, said in a note.
"What this means for Fed policy is anyone's guess of course at this point but the market is clearly not expecting anything in October and only a 30 percent chance by December," he said.
The final Markit PMI services index for September came in at 55.1, below August's 56.1 and the lowest read since June.
Treasury yields held higher, with the 10-year yield at 2.06 percent and the 2-year yield at 0.61 percent in the close.
The U.S. dollar traded higher against major world currencies, with the euro below $1.12 and the yen at 120.42 yen against the greenback.
The U.S., Japan and 10 other Pacific Rim countries reached an agreement Monday for the years-in-the-making Trans Pacific Partnership. The trade deal still needs final approval from Congress.
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Shares of Twitter surged nearly 7 percent, attempting to top its 50-day moving average of $27.85 a share, on news the social media firm named Jack Dorsey permanent CEO.
Shares of Alphabet, the new umbrella company for Google, jumped in their first few minutes of trading Monday.
Both Class A and Class C of Alphabet shares were about 2 percent higher in afternoon trade. Alphabet is identical to Google from a stock market perspective.
Alcoa leaped 9.35 percent for its best day since Oct. 27, 2011, on news of a $1 billion deal with Airbus.