Greek authorities say more than 7,800 coronavirus tests were carried out on passengers who arrived at Athens international Airport last week and turned up four cases.
Authorities said the 7,804 checks were carried out on flights that arrived June 8-14, before Greece opened to most European tourists this week without compulsory coronavirus tests.
Greece has been eager to promote itself as a safe tourist destination, and to salvage what is left of the summer tourist season. The country is heavily dependent on tourism, which makes up around 20% of its economy.
Tourists have been able to fly into Athens and the northern city of Thessaloniki since Monday, and are subject to random coronavirus tests rather than mandatory testing and quarantine.
International flights will be able to fly directly to regional airports from July 1.