There were 19.2 million jobless people in the region, up by 1.3 million from a year earlier, according to Eurostat, the single-currency zone's statistical office. The unemployment rate was 11.3 percent in May 2012.
Inflation in the region increased at a 1.4 percent annual rate in May, up from 1.2 percent the previous month, Eurostat said in a separate report. The figure is below the European Central Bank's target of 2 percent annual price growth.
Eurostat initially had reported a 12.2 percent unemployment rate for April, but that figure was revised to 12 percent on Monday, making May's 12.1 percent the new high since the eurozone was created in 1999.
The revisions mean the European unemployment picture is better than expected, said Howard Archer, chief economist for Europe and Britain at IHS Global Insight.
But there were 67,000 more people out of work in May than in the previous month, he noted.
"The still marked rise in eurozone unemployment in May highlights the fact that the eurozone continues to face major head winds and still has its work cut out to return to growth," Archer said.
Spain had the highest May unemployment rate, at 26.9 percent. Greece had a 26.8 percent unemployment rate in March, the latest figure available for that nation.
Austria had the region's lowest jobless rate, at 4.7 percent, followed by Germany at 5.3 percent.
The U.S. unemployment rate was 7.6 percent in May. That figure is projected to have dipped to 7.5 percent in June; the Labor Department will release its June jobs report Friday.
The eurozone's economy has been in recession for six straight quarters through the first quarter of the year. That topped the 2008-2009 recession, which lasted for five quarters.
Austerity measures designed to help several eurozone nations deal with debt problems have pushed the region back into recession while the U.S. economy has been growing -- albeit slowly -- since mid-2009.
The economic problems in Europe hurt the U.S. by reducing demand for imports from across the Atlantic.