Greek Health Ministry representative Sotiris Tsiodras on Tuesday announced 48 new cases of the coronavirus, bringing the total nationwide to 743.
Another three infected people died, pushing the death toll 20.
Of those infected, 134 are in hospital with 45 in critical condition, Tsiodras said.
Noting that one of the victims in Greece had died at home before being diagnosed, Tsiodras said it was important that all those with underlying medical conditions, irrespective of their age, should be in contact with their doctor if they display symptoms of the virus, namely a fever, a dry cough, respiratory problems or a loss of their sense of taste.
Notwithstanding the new cases, Tsiodras expressed a cautious optimism that, for the moment at least, Greece does not appear to be heading to the sharp increase that has been observed in other countries.
Also, despite increases in the transmission of the virus worldwide, Tsiodras pointed to two positive developments further afield: a reduction in cases and deaths in Italy, the European country worst hit by the virus, and the lifting of restrictions as of Wednesday in Wuhan, the Chinese epicenter of the pandemic following zero new cases in the past five days.