Survey compiler Markit said on Wednesday its Eurozone Composite PMI, which gauges business activity across thousands of companies in the 17-nation currency bloc, rose last month to a reading of 46.5 from 45.7 in October.
That marks a big improvement from a preliminary reading released 10 days ago, but there are few signs the region will emerge from recession any time soon. A reading below 50 indicates contraction.
Markit said the readings still pointed to a deepening of the euro zone's recession during the last three months of this year. Many economists expect the recession to stretch into early 2013.
"We see no signs of improvement that suggest that the (euro zone) economy might recover any time soon. Further contraction in GDP remains our baseline scenario at least until Q1 2013," said Annalisa Piazza, economist at Newedge Strategy in London.
Growth in China's services sector slowed in November as lackluster growth in new orders and a surge of recent hires reduced work backlogs.
The HSBC Purchasing Managers Index for China's services sector released showed the index slipped to 52.1 in November from October's 53.5, as sales prices continued to fall despite a rise in input prices.