By Paul Hannon

Consumer prices in the 28-member European Union rose at the slowest pace for four-and-a-half years in the 12 months to March, indicating that falling inflation rates are a problem for economies throughout the continent, and not just those that share the euro.

The European Union's statistics agency Wednesday said consumer prices in the 18 nations that share the euro were 0.9% higher than in February, and 0.5% higher than in March 2013. That confirmed the preliminary estimate released late last month, and is the lowest annual rate of inflation since November 2009.

Eurostat said the core rate of inflation--which strips out volatile items such as energy and food--slipped to 0.7% from 1.0% in February, matching the record low reached in December 2013.

Eurostat also said the annual rate of inflation in the broader EU--which includes 10 countries that don't use the euro--fell to 0.6% from 0.8% in February, its lowest level since October 2009.

Eurostat's figures show that five euro-zone members experienced declines in prices in the 12 months through March, while three members of the EU that don't use the euro shared the same experience. But other members were on the cusp, with four euro-zone members recording inflation rates below 0.5%, as did four EU members that don't use the euro. Of the EU's 28 members, only one had an inflation rate in excess of 1.5%: the U.K., where prices rose 1.6% in the 12 months to March.

The slowdown in inflation is a mixed blessing. While it should help boost real incomes at a time of weak wage growth, it also raises the specter of deflation--a sustained and self-reinforcing fall in prices that can play havoc with public and private efforts to repay debts and risks bringing consumer spending to a halt.

Policy makers at the European Central Bank have repeatedly said they don't expect to see a period of falling prices across the currency area as a whole. They reject comparisons with Japan, which struggled with deflation for two decades, saying the ECB has acted more decisively than Japan did in the 1990s and that European banks are stronger.

But they have acknowledged that very low rates of inflation are a worry, and in recent weeks have focused on the role of an appreciating euro in pressing down on import prices and activity.

ECB President Mario Draghi Saturday ratcheted up his warnings about the strong euro, saying a further rise in the exchange rate against other currencies would trigger additional monetary easing to keep inflation from falling too low.

"A strengthening of the exchange rate requires further monetary stimulus. That is an important dimension for our price stability," Mr. Draghi said at a news conference during meetings of the International Monetary Fund.

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