The number of unemployed rose 95,000 to 19.38 million. The currency bloc's population is about 330 million.
Private companies in the eurozone haven't managed to fill the vacuum created by drastically reduced government spending. In the United States, by contrast, governments have imposed far milder spending cuts and tax increases. Unemployment, at 7.5 percent, is far lower. And consumers and private companies have kept spending, steadily if modestly.
The unemployment rate for the overall eurozone masks sharp disparities among individual countries. Unemployment in Greece and Spain top 25 percent. In Germany, the rate is a low 5.4 percent.
The differences are particularly stark for youth unemployment. More than half of people ages 16 to 25 in Greece and Spain are unemployed. In Italy, the rate for this group tops 40 percent. For Germany, it's just 7.5 percent.
"Youth joblessness at these levels risks permanently entrenched unemployment, lowering the rate of sustainable growth in the future," said Tom Rogers, senior economic adviser at Ernst & Young.
The disparities reflect the varying performances of the euro economies. Greece is in its sixth year of a savage recession. Germany's economy has until recently been growing at a healthy pace.
As a whole, the eurozone is stuck in its longest recession since the euro was launched in 1999. The six quarters of economic decline represent a longer recession than the one that followed the 2008 financial crisis, though it's not as deep.
The U.S. economy, the world's largest, has demonstrated far more resilience. It's grown steadily since the end of its recession in June 2009. And the U.S. job market has steadily improved: The unemployment rate has fallen sharply from a peak of 10 percent.
The eurozone marks the epicenter of Europe's debt crisis. But other countries in the region are also struggling to recover. Some, like Britain, are focused on shrinking their deficits even while demand in their main export market the eurozone is falling.
As a result, unemployment in the wider 27-nation EU, which includes the non-euro countries such as Britain and Poland, has risen in recent months. In April, the rate remained 11 percent.
A key factor behind Europe's economic decline has been a broad focus on paring debt by raising taxes and slashing spending. As long as many governments continue to cut spending and the confidence of consumers and businesses remains low, economists don't expect any meaningful recovery in coming months.
Friday's data showed that the sharpest change in unemployment rates among the 17 euro countries was in Cyprus. Its unemployment rate jumped to 15.6 percent from 14.5 percent.
The small Mediterranean island nation became the fifth euro country to seek financial help in March. Unlike with other bailouts, Cyprus was asked to raise much of its rescue money from bank depositors. That decision led to a nearly two-week shutdown of its banks and battered economic confidence.
The European Central Bank has sought to ease the pressure on Europe's businesses and consumers by cutting its main interest rate to a record low 0.5 percent this month. Another cut is possible. But most economists say it's unlikely, even though the inflation rate remains under the ECB's target of just below 2 percent.
Eurostat said inflation in the eurozone rose to 1.4 percent for the year that ended in May, from the 38-month low of 1.2 percent in April. It attributed the increase to rising food, alcohol and tobacco prices.
Analysts said the ECB is more likely to act to shore up lending to small and medium-sized businesses, which are key job creators in Europe. Such companies are taking out few loans out of fear that the economy might worsen and because banks are charging high rates.
"So far, the ECB's actions have not translated into lower lending rates for businesses and households, failing to boost activity," said Anna Zabrodzka, economist at Moody's Analytics.