Greece announced two more coronavirus deaths on Saturday bringing the toll to three, as an unprecedented lockdown takes effect.
A 67-year-old man died on Zakynthos island early on Saturday and a 90-year-old man died in the northern city of Ptolemaida, the health ministry said.
Both men had health problems.
The man in Zakinthos was believed to have contracted the virus after visiting a hospital in western Greece where the first fatality was confirmed, Athens News Agency reported.
Greece closed shops, bars and restaurants on Friday as well tourist sites such as the Acropolis as coronavirus cases jumped from 117 to 190.
Only supermarkets, pharmacies and medical facilities have been allowed to stay open.
The government had already shut down schools and universities, courts, cinemas, gyms and other indoor public gathering areas for two weeks in an effort to curb the outbreak.
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A torch relay for the Tokyo 2020 Games has been cancelled after Hollywood actor Gerard Butler, who starred as the ancient Spartan King Leonidas in the 2007 epic "300", was mobbed as he lit a cauldron in the city of Sparta.
The Greek Olympic Committee said crowds had ignored "repeated warnings" not to gather at stopovers in the torch relay.
The flame for the 2020 Tokyo Games was lit in ancient Olympia on Thursday without spectators after dozens of people tested positive for COVID-19 in the region.
Meanwhile, Greek government spokesman Stelios Petsas said his wife had tested positive for the coronavirus and he would self-isolate for two weeks as a precaution.