Markit said the purchasing managers index for goods-oriented producers reached 52.7 in the month, modestly higher than the 50 percent break-even point that stands between growth and contraction.
Markit said rising production and "fuller order books" in the month encouraged manufacturers to hold off on announcing further job cuts.
Fresh orders for exports rose "at a solid pace," Markit said, noting that the headline index showed growth for the entire second half of 2013.
The PMI for France, the second largest economy in the 17-nation eurozone, fell to a 7-month low at 47, Markit said. But the index for Germany, Italy, Spain Greece, the Netherlands, Austria and Ireland all rose.
Germany's PMI climbed to 54.3, a 30-month high. The index for the Netherlands hit 57, a 32-month high.
At 53.3, the index in Italy reached a 32-month high and for Greece, the index showed business contraction at 49.6. Nevertheless, for Greece, the index for December is at a 52-month high, Markit said.