The number of officially unemployed reached 1.124 million people. Hardest hit were young people aged 15 to 24 years, with their jobless rate easing to 47.7 percent from 48.2 percent in the same month a year earlier.
The reading in June, based on seasonally adjusted data, was the lowest since April 2012 when unemployment stood at similar levels. The jobless rate hit a record high of 27.9 percent in September 2013.
Greece's jobless rate has come down from record highs but remains more than double the euro zone's average of 10.1 percent in June.
The economy expanded by a modest 0.2 percent in April-to-June compared to the first quarter but is expected to remain in recession this year as the country feels the full brunt of austerity measures approved under its third bailout.