A total of 209 deaths have been recorded.
Greece instituted an early lockdown in mid-March, which protected the country from the devastating effects of the pandemic seen in many other European countries.
But the recent increase in infections has prompted authorities to introduce measures such as mandatory face masks in confined spaces.
Professor Sotiris Tsiodras, who gave his first public briefing after a hiatus of more than two months, said there had been no pressure on the public health system, but warned the situation without vigilance could spiral out of control.
There must be great vigilance for a possible increase. The situation could quickly get out of hand. He needs everyone’s vigilance and attention.
There have been clusters of epidemics, he said, at one meat processing unit and at two marriages. In the past two months, he said, there has been a “clear shift” towards the virus affecting young people.
Many were symptom-free, he said, adding that cases were detected after Greece reopened its borders in June. But he said an outbreak between July 31 and August 2 appeared to be household infections.