The jobless rate rose to 24.4 percent from a revised 23.5 percent in the previous month, statistics service ELSTAT said on Thursday.
The Greek jobless rate is now just a fraction behind the level in fellow euro zone sufferer Spain, whose unemployment rate for the three months to June stood at 24.6 percent, according to Madrid's official figures.
A total of 1.2 million Greeks were without work in June, up 42 percent from the same month last year.
Budget cuts imposed by the European Union and the International Monetary Fund as a condition for saving the debt-laden country from a chaotic default have aggravated a wave of corporate closures and bankruptcies.
Credit to companies has been shrinking as the country's banks depend on the ECB for liquidity and cannot fund firms.
The impact has been felt hardest on those aged between 15-24 years. Unemployment in that age group stood at 55 percent, compared with 20 percent in 2008, when Greece's recession began.
Greece's economy is estimated to have shrunk by about a fifth since then. More than 600,000 jobs, more than one in 10, have been destroyed in the process.
The slump is expected to accelerate later this year if the government implements further budget cuts of almost 12 billion euros over the next two years as a pre-condition for more funds under its EU/IMF bailout.
(Reporting by Harry Papachristou; editing by Stephen Nisbet)
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