The European Union's statistics office Eurostat said consumer inflation in the 19 countries sharing the euro was 0.4 percent month-on-month in December and 1.4 percent year-on-year, down from 1.5 percent in November.

Of all components, energy prices rose the most at 2.9 percent year-on-year in December, while unprocessed food gained 1.9 percent. Without these two volatile components, or what the ECB calls core inflation, prices rose by 1.1 percent year-on-year, the same as in November and in October.

Some economists believe that a better measure of core inflation is the one that takes out not only energy and unprocessed food but also alcohol and tobacco, the prices of which are often influenced by government tax changes.

But this measure also held stable at 0.9 percent in December, unchanged form the previous two months.

The ECB wants to keep inflation below but close to 2 percent over the medium-term and has been buying government bonds on the secondary market to inject more cash into the banking system and so to stimulate credit to the economy.

But while the euro zone economy is growing at its fastest pace in a decade and unemployment is at nine-year lows, this has not yet translated into significantly faster price growth.

(Reporting By Jan Strupczewski; editing by Philip Blenkinsop)