The Markit Eurozone Purchasing Managers' Index reached a nine-month high in December, stated the firm's flash estimate, which was at 47.3 from 46.5 in November.
The PMI suggests the downturn may have reached its strongest in October, although the survey continues to signal a steep overall rate of decline, with business activity levels having fallen in 15 of the past 16 months.
Markit said the turnaround is being led by Germany, for which the PMI has returned to positive territory. The rates of decline in France and the rest of the region, however, remain "worryingly severe," Markit chief economist Chris Williamson said Friday in statement.
Output rose for the first time in eight months in Germany, though an upturn in the service sector was offset by a faster decline in manufacturing production. Output fell for the 10th consecutive month in France but the rate of decline was the slowest since August.
Looking at the entire eurozone, output continued to fall in manufacturing and services, though in both cases the rate of decline showed signs of moderating. Although goods production fell at a pace unchanged in November, the previous month's decline was the smallest for seven months. The rate of decline in service sector activity, meanwhile, eased to its weakest since July.
The rate of decline of new business slowed for the third month in a row, indicating companies continued to face steeply deteriorating demand for goods and services, Markit said.
The rate of job losses slowed in December, hitting the lowest since August.
Optimism jumped to a seven-month high in Germany and edged up to a four-month peak in France but fell back slightly elsewhere across the eurozone.
"The eurozone downturn showed further signs of easing in December, adding to hopes that the outlook for next year is brightening. It looks like the downturn reached its fiercest back in October, since when the PMI has turned up steadily by no means spectacularly," Williamson said.
Williamson said a return to growth "is looking like an increasing possibility in the first half of next year, barring any surprises, if the recent improvements in the survey data can be sustained."