By Paul Hannon 

Activity in the eurozone's private sector picked up slightly in October, although businesses cut their prices at the fastest pace since early 2010, making it more likely the European Central Bank will soon have to announce a third wave of stimulus measures.

Data firm Markit Thursday said its monthly composite purchasing managers index--a measure of activity in the manufacturing and services sectors in the currency bloc--rose to 52.2 from 52.0 in September. A reading below 50.0 indicates activity is declining, while a reading above that level indicates it is increasing.

However, the survey of 5,000 manufacturers and service providers also suggested that a further significant pickup is unlikely in coming months, with new orders barely rising, while businesses cut jobs for the first time since November 2013.

"The eurozone PMI rose in October but anyone just watching the headline number misses the darker picture painted by the survey's other indexes, which show the region teetering on the verge of another downturn," said Chris Williamson, chief economist at Markit.

The surveys therefore offer little relief for policy makers beyond the eurozone's borders. The specter of deflation in Europe and a slowdown in China and other emerging markets are threatening to hobble the U.S. economy at a time when the world could use a reliable growth engine. An equivalent gauge of activity in China's manufacturing sector also rose in October, a result which may go some way in easing concerns over the pace of Chinese economic growth.

The eurozone's two largest economies continued to diverge. While German surveys pointed to a slight acceleration of activity, French surveys pointed to a deepening decline. The French survey also indicated that a recovery is unlikely soon, with new orders falling and businesses cutting jobs for the 12th straight month. In contrast, German manufacturers hired workers at the fastest pace in almost three years.

Their diverging economic performances have led to political tensions between the two nations at the heart of the euro project. The French government has urged its German counterpart to invest an additional EUR50 billion ($63.8 billion) over three years as a way of countering budget cuts in France.

But in Berlin, policy makers are sticking to the view that the eurozone crisis and sluggish growth result from a lack of sufficient economic overhauls in struggling countries, especially France and Italy.

The surveys of purchasing managers show that what France and Germany have in common is the threat of a slide into deflation, or a period of self-reinforcing price declines. French businesses cut their prices at the sharpest pace in five years, while German businesses cut theirs for the first time since June 2013. Across the eurozone as a whole, prices were cut at a rate not seen since February 2010.

The ECB has since June undertaken a series of stimulus measures in an effort to boost inflation, including record-low interest rates, a new bank lending facility and a program to buy covered bonds. It will soon start to buy asset-backed securities.

But the central bank is also considering purchasing corporate bonds if it concludes that more aggressive measures are needed to pump additional money into the eurozone's fragile economy and raise inflation from its superlow levels.

ECB member Yves Mersch said Wednesday the eurozone economy is still fragile and risks of additional economic setbacks remain.

"The overall situation of the European economy makes it abundantly clear that we cannot wait for a miracle to end a period of low growth," Mr. Mersch said. "We aren't out of the danger zone. The patient is still fragile and, unfortunately, relapses cannot be ruled out."

Write to Paul Hannon at paul.hannon@wsj.com