Eurozone economic activity slowed in the first weeks of 2016, according to surveys of purchasing managers, a development that adds to mounting concerns about the weakness of the global economy amid sharp declines in the prices of commodities and financial assets.

Despite the concerns of policy makers, the eurozone’s recovery showed few signs of being weakened by slowdowns in China and other large developing economies in the final months of 2015. But there are hints that it is beginning to succumb to external forces.

There are also indications that the decline in oil prices since the start of the year has weakened the outlook for inflation in the eurozone, since the purchasing managers reported cutting their prices at the fastest pace in 10 months.

European Central Bank President Mario Draghi Thursday signaled that the governing council may provide more stimulus at its next meeting in March, noting that the outlook for inflation had weakened “significantly” and that the eurozone economy may slow.

Data provider Markit said a headline measure of activity based on surveys of 5,000 companies around the eurozone, known as the composite purchasing managers index, fell to 53.5 in January from 54.3 in December. A reading above 50.0 indicates an increase in activity, while a reading below that level indicates a decline.

The January reading still points to a rate of expansion that is broadly in line with the eurozone’s economic performance since it returned to modest growth in mid-2013. But there will be concerns that the longer turmoil in financial markets persists, the greater the threat to the recovery will be.

A measure of consumer confidence released by the European Commission Thursday recorded a decline in optimism in January, the first since October.

The eurozone economy slowed in the three months to September, growing by just 0.3% from the previous three-month period. Surveys and data releases for the fourth quarter suggest that it may have rebounded slightly as 2015 drew to a close.

Falling oil prices have boosted household spending power, while steady declines in unemployment have also supported domestic demand and provided some insulation from setbacks elsewhere in the global economy. Speaking at a news conference Thursday, Mr. Draghi said the stimulus measures announced by the ECB since June 2014 should make the eurozone economy more resilient to fresh shocks.

Indeed, the International Monetary Fund Tuesday raised its economic growth forecasts for 2016 to 1.7% from the 1.6% projected in October, even as it lowered its forecast for the global economy.

“It would be wrong to get too worried,” said Chris Williamson, Markit’s chief economist. “Firms appear to be looking to brighter times ahead, with business confidence improving, linked in turn to backlogs of work rising at the fastest rate since the spring of 2011. With plenty of orders in hand to work through, hiring remained encouragingly resilient at the start of the year.”

But however resilient the eurozone is, growth is unlikely to be strong enough to quickly raise the annual rate of inflation to the ECB’s target of just under 2% from the 0.2% recorded in December. ECB economists in December forecast that consumer prices would rise by 1% this year, but oil prices have fallen by 40% since then and Mr. Draghi said the outlook for inflation has weakened “significantly.”

Some economists now expect prices to start falling again in February, and record barely any increase over the year.

In Markit’s survey, businesses reported that the decline in their costs was the second-largest since July 2009, during the depths of the global downturn that followed the 2008 financial crisis. That reflected falling oil prices, and should boost profit margins in the near term.

But businesses passed some of the declines in their costs onto customers, once again cutting the prices they charge in a manner that will raise concerns at the ECB. Mr. Draghi Thursday said policy makers are particularly worried that the longer oil prices remain low, the more likely it is that prices of other goods and services will also fall as a consequence of what central bankers call “second round effects.”

The surveys recorded a slight rebound for France’s economy after an end-of-year slowdown following the Nov. 13 terror attacks in Paris and a subsequent tightening of security around the country. The composite PMI for France rose to 50.5 from 50.1 in December, but was below its levels before the attacks.

However, activity in Germany slowed, with the composite PMI falling to 54.5 from 55.5.