Eurostat, the EU's statistics office, said unemployment across the eurozone fell to 18.91 million in March from 18.94 million the month before. Though not a dramatic fall, it is a further improvement from last April's peak of 19.24 million.
The unemployment rate, however, was unchanged at 11.8 percent for the third month running following downward revisions to previous data largely due to Spanish census data. Again, as in the number of unemployed, the rate is down on the eurozone's record, reached in 2013, of 12 percent.
Timo del Carpio, European economist at RBC Capital Markets, said the figures "lend more weight to the view that unemployment in the euro area peaked late last year, which will offer some degree of reassurance to policymakers that the recovery is slowly gaining traction."
Most economists expect unemployment to carry on falling, albeit modestly, over the months ahead as the economic recovery gathers pace unemployment figures often lag growth.
Figures later this month are set to confirm that the eurozone grew in the first three months of the year, for the third quarter running.
A number of surveys have indicated that the pace of growth may double from the 0.2 percent quarter-on-quarter rate recorded in the last three months of 2013. One of the main reasons behind the pick-up is that the financial stresses have eased in a number of the more indebted countries, such as Greece and Spain, following years of spending cuts and tax increases.
The overall figures continue to mask huge discrepancies that are found both across the region and between generations and likely to take years to unwind. Despite the more favorable economic backdrop, many governments will have to continue to keep government spending tight for many more years to improve public finances.
While Germany's unemployment rate is 5.1 percent, others, notably those countries at the forefront of the crisis, have double-digit rates. Greece and Spain are the two countries that have the most work to do to bring unemployment down, but even here improvements were evident.
In Greece, the first eurozone country to descend into the debt crisis abyss, unemployment rate in January was 26.7 percent, down on the previous month's 27.2 percent. Greek figures are compiled on a delayed basis. And among workers under the age of 25, the jobless rate was 56.8 percent against 57.1 percent.
In Spain, which unlike Greece did not need an international bailout but has suffered as the government pursued an austerity policy following the collapse of a property bubble, unemployment was steady at 25.3 percent in March, down a full percentage point from a year ago. Among the young, the rate was unchanged from a month earlier at 53.9 percent, but down on last year's rate of 55.4 percent.