Panagiotis Papanikolaou, the secretary of the Federation of Hospital Doctors' Associations of Greece, said: "We said there was a problem in informing the public as far as the geographical distribution of cases is concerned. It is unacceptable."
He also accused international tour operators of "strong-arming the Government" into downplaying the number of cases on the islands.
Yiannis Ragousis, an MP with the opposition Syriza Party, accused the Government of deliberately concealing island cases, and of endangering the health of "tens of thousands of people".
He said: "They knew what was going on, and said nothing, neither to residents nor to visitors. Their excuse that they didn't want to defame any particular island cannot convince anyone."
A swift, early lockdown meant Greece has recorded 10,500 cases and 271 deaths.
In the seven days to September 1, Greece recorded 14.3 cases per 100,000 people, up marginally from 14.1 a week earlier.