The seasonally adjusted jobless rate for the single-currency region was 6.2% for the second month in a row, matching the all-time low levels seen briefly during the end of 2024.
Some 10.986m people were unemployed in May, down 55,000 over the month and 158,000 lower than a year ago.
Meanwhile, youth unemployment fell by 12,000 over the month, keeping the jobless rate for those under 25 at 14.7%.
Across the 21 eurozone member states, the lowest recorded unemployment rates were in Bulgaria (2.9%) and Cyprus (3.1%), while the highest rates were registered in Spain (10.3%) and Greece (9.1%).