Economists said the lack of any real improvement is troubling, despite proclamations by some European politicians that the worst of the continent's economic crisis is behind it.
"May's unemployment data highlight that the eurozone's economic recovery is still too weak to erode the significant amount of slack in the labour market," said Jessica Hinds of Capital Economics in a research note.
Divergence remains strong between the countries of northern and southern Europe: German unemployment was 5.1 percent, while Italy's was 12.6 percent, Spain's 25.1 percent, and Greece's 26.8 percent — though Greece is still reporting March figures.
The situation is only slightly better in the wider European Union, which includes non-euro countries like Britain and Sweden. There, the unemployment rate edged down to 10.3 percent from 10.4 percent the month before.
By comparison, the U.S. unemployment rate was at 6.3 percent in May.
European Central Bank President Mario Draghi has said that among his greatest worries is that high unemployment in the eurozone, a problem for years, becomes entrenched. When a large part of the labor force is out of work for an extended period of time, people fail to gain new skills they need to be productive and help the economy grow.
The ECB last month announced a string of measures to help the eurozone economy and nudge up inflation, which is languishing at a low 0.5 percent rate. But the central bank, which will meet again on Thursday, has stressed that governments should also act to ease unemployment by reforming their economies, cutting red tape and bureaucracy.
Economist Bill Adams of PNC Financial Services Group said the ECB will likely not act again this week but predicited it "sooner or later will have to confront the uncomfortable likelihood that significantly more action is needed."
Tuesday's report showed youth unemployment in particular remains a grave problem, at 23.3 percent across the eurozone. It is at crisis levels in southern Europe, with both Spain and Greece showing unemployment rates for people under the age of 25 at over 50 percent.