The economic crisis in southern Europe may be easing, a key survey signalled on Monday, but new data showed the eurozone jobless rate returned to a record high of 12.1 percent in May.
There are signs too that economies in eastern/central Europe may be on the mend.
The Eurostat figures offered little hope of a quick end to the social crisis, with the unemployment rate for the entire European Union being unchanged at 10.9 percent.
Eurostat said 26.4 million Europeans are now out of work.
Provisional official data in Italy showed the jobless rate hitting a new record of 12.2 percent.
EU leaders agreed to deploy up to 8.0 billion euros ($10.4 billion) in programmes to fight youth unemployment at a summit in Brussels last week after US President Barack Obama warned of the risk of a "lost generation" in Europe.
The Eurostat report, which revised previous figures, showed the eurozone rate reached 12.1 percent in March.
It then edged down to 12.0 percent in April -- a slight improvement that ended two years of increases -- but then rose in May.
The results were far worse than in May of last year, when eurozone unemployment was at 11.3 percent and the EU rate at 10.4 percent.
For under-25s the picture was even bleaker, with the rate rising to 23.0 percent for the EU as a whole from 22.8 percent in May 2012.In the eurozone, it rose to 23.8 percent from 23.0 percent.
There were wide differences between EU members. Unemployment fell in May in 10 countries on a 12-month comparison.
The best results were in Latvia, where the rate fell to 12.4 percent from 15.5 percent, and in Estonia where it went down to 8.3 percent from 10.0 percent.
The worst was Cyprus, where the banking sector is being cut radically and where the jobless rate rose to 16.3 percent in May 2013 from 11.4 percent in May 2012.
Unemployment data is a lagging indicator. In a separate set of figures, eurozone manufacturing showed signs of continued improvement in June.
The Markit Eurozone Composite Purchasing Managers Index, a survey of what businesses see happening in their production processes, rose to 48.8 in June -- a 16-month high -- from 48.3 in May.
-- 'Fragile recovery': analyst --The PMI index is considered to be a reliable indicator of future activity.
Ireland saw an improvement and Spain remained stable, while the rates of contraction eased in Austria, France, Greece, Italy and the Netherlands.
"Strong improvements in Spain, Italy and France more than offset a mild German setback as exporters there struggle with weakness in China and competition from Japan," said Christian Schulz, an economist at Berenberg Bank.
"On current trends, the end of recession in the crisis countries is approaching fast. Spain's manufacturing PMI left contraction territory for the first time since April 2011 and Italy was not far behind," he said.
The PMIs for Italy and Spain were higher than Germany's for the first time since the eurozone debt crisis reached its peak in 2011.
Meanwhile, William Jackson, the emerging markets economist at Capital Economics in London, said that the latest batch of PMI indicators for several countries in central Europe added "to the growing sense that things are improving in the region."
But he observed: "Even so, we still expect the recovery to be pretty lacklustre."
Jonathan Loynes, chief European economist at Capital Economics, was cautious, pointing to unemployment and inflation data on Monday which he said underlined the "fragile recovery" in Europe.
"The latest eurozone inflation and labour market figures inject a slight note of caution," he said.
"There is nothing here to suggest that the eurozone economy does not need additional policy support, though the ECB (European Central Bank) looks unlikely to oblige this week" at its monthly policy meeting, he said.
Eurozone inflation accelerated to 1.6 percent in June from 1.4 percent in May largely due to higher energy prices, Eurostat said, but is still a long way from the target set by the ECB of keeping inflation at just below 2.0 percent.