The Institute of Supply Management said its gauge of the U.S. service sector, which employs 90 percent of the work force, grew for the 22nd consecutive month. The index measures the strength of health care providers, banks, real estate, and other businesses outside of manufacturing.
Payroll processor ADP said private companies added 91,000 jobs last month. That was a slight gain from August. ADP's figures do not always predict what the government's broad employment report, which will be released Friday, but they can often influence traders' expectations.
At 11 a.m. Eastern, the Dow Jones industrial average was up 73 points, or 0.7 percent, to 10,881. The Standard and Poor's 500 index was up 9, or 0.9 percent, to 1,133. The Nasdaq composite rose 30, or 1.3 percent, to 2,435.
The latest indications of growth in the U.S. economy pushed Treasury prices lower as investors moved money out of lower-risk investments. The yield on the 10-year Treasury rose to 1.89 percent from 1.82 percent late Tuesday.
European indexes rose broadly following reports that European officials are exploring a joint effort to support the region's struggling banks. That could limit the damage to the financial system should the Greek government default on its debt, which many traders expect. The reports, which came out after European markets closed Tuesday, triggered a late rally in U.S. stocks that prevented the S&P 500 from entering a bear market.
Seed company Monsanto rose 2 percent after it announced that its fourth-quarter results beat Wall Street's expectations. Wholesale club operator Costco Wholesale Corp. dropped 2 percent after its earnings came in at $1.08 per share, slightly below analyst's expectations of $1.10 per share. The company said it will raise its annual membership fees in November.
Apple Inc. lost 2.5 percent, a day after the company announced an updated version of the iPhone that disappointed some analysts. Apple announced an upgrade to its iPhone 4, but many were expecting the iPhone 5.