The Institute of Supply Management said the Purchasing Management Index for April came to 54.8 percent. Economists had expected a more subdued 53 percent -- figures above 50 indicating growth.
By close of trading on Wall Street, the Dow Jones industrial average added 65.69 points, 0.5 percent, to 13,279.32. The Nasdaq composite index gained 4.08 points, or 0.13 percent, to 3,050.44.
The Standard and Poor's 500 index tacked on 7.91 points, or 0.57 percent, to 1,405.82.
On the New York Stock Exchange, 1,961 stocks advanced and 1,097 declined on a volume of 3.6 billion shares traded.
The 10-year treasury note lost was yielding 1.948 percent.
The euro fell to $1.3236 from Monday's $1.3239 while the dollar rose to 80.17 yen from Monday's 79.82 yen.
In Tokyo, the Nikkei 224 index shed 1.78 percent, 169.94, to 9,350.95 after a one-day holiday.
In London, the FTSE 100 index added 1.3 percent, 74.45, to 5,812.23.
Notable deaths of 2014 [PHOTOS]
GM recalls 221,000 Cadillacs and Impalas