Greece has said it will open to visitors from 29 countries from 15 June, days before its peak tourism season begins, although Ireland is not on the list of countries.
The countries are: Germany, Austria, Denmark, Norway, Cyprus, Israel, Switzerland, Japan, Malta, Bulgaria, China, Croatia, Australia, New Zealand, North Macedonia, Albania, Estonia, Latvia, Lebanon, Lithuania, Hungary, South Korea, Serbia, Montenegro, Romania, Slovenia, Slovakia, Czech Republic and Finland.
Visitors will be randomly tested, the tourism ministry said, and the government would monitor and evaluate developments related to the coronavirus. The list will be updated before 1 July, the tourism ministry said.
The Mediterranean nation, which emerged from a decade-long debt crisis in late 2018, relies heavily on tourism - about 20% of its output - for an economic recovery.
A nationwide lockdown imposed in March helped Greece contain the spread of Covid-19 infections to just below 3,000 cases, a relatively low number compared with elsewhere in the European Union. But it brought its business and tourism sector to a virtual standstill.
About 33 million tourists visited Greece last year, generating revenues of €19bn.
The Irish Chief Medical Officer, Dr Tony Holohan, has said he was not aware of any communication between Greek and Irish health officials and was unaware of what criteria Greece used to restrict travel from Ireland.
"Our rate of infection might look comparatively high in relation to other countries, we're testing at a much higher level. In fact, we have much higher assurance than many other European countries have," he said.
"We have been testing as much as possible. We're now also testing contacts. There are very few countries, including Greece, that are able to do that," he added.
Bulgaria has said it will lift an obligatory 14-day quarantine from 1 June for travellers from most European Union countries, but not those states with the biggest coronavirus outbreaks, the government announced on Friday.
The quarantine will remain obligatory for travellers from Sweden, Belgium, Ireland, Portugal, Spain, Italy and Malta, as well as the UK, which is in a transition period after leaving the EU, according to an order issued by Health Minister Kiril Ananiev.
A ban on the entry of visitors from outside the EU will remain in place, although there will be exemptions for citizens of the Schengen zone countries, the United Kingdom, San Marino, Andorra, Monaco, Vatican City as well as Serbia and North Macedonia.
Bulgaria has eased most of the restrictive measures it imposed in March to combat the coronavirus spread, allowing restaurants, cafes, gyms and theatres to reopen and lifting a ban on travel between cities.
Last week it lifted a ban on the entry of citizens from EU countries, but imposed a 14-day quarantine.
By allowing visitors from other parts of the EU it hopes to restore trade and boost summer tourism to its Black Sea resorts, hard hit by the lockdown.