Greece is to open up to tourists from 29 countries in two weeks - but not those travelling from the UK.
Tourists from EU countries including Germany, Austria, Denmark and Finland will be able to visit from 15 June, the tourism ministry said in a statement on Friday.
But some of the world's worst-affected countries - including the UK, France, Italy and Spain - are not on the list.
More countries could be added before 1 July, the ministry added.
Only airports in Athens and Thessaloniki will open on 15 June. Tourists from 16 EU countries will be allowed into the country, including the Czech Republic, Baltic countries, Cyprus and Malta.
Other countries include China, Japan, Australia, New Zealand, South Korea, Israel and Lebanon.
Some visitors could be tested for Covid-19 on arrival, the ministry said.
"Our aim is to be able to welcome every tourist who has overcome their fear and has the ability to travel to our country," Tourism Minister Harry Theoharis said on Antenna television.
Greece, which imposed an early lockdown, has reported 175 deaths and just over 2,900 confirmed cases. Most of the country's islands have no reported cases.