Primary school children have also returned to class as the country ramps up preparations for the crucial summer tourism season to start in two weeks.

Strict public safety measures have kept Greece's COVID-19 infection rate low. The country has suffered only 175 virus-related deaths, according to Health Ministry data.

International flights with screening procedures will return to Athens and Greece's second-largest city of Thessaloniki starting on June 15 and will be expanded to the rest of the country on July 1.

Screening for arriving passengers will be based on an assessment by a European Union flight safety authority, with arrivals from low-infection countries being subjected only to random testing.

"Greece is continuously monitoring epidemiological data, in collaboration with experts and European and international organisations," government spokesman Stelios Petsas said. "We will receive visitors from countries that are improving in their infection curve and remain vigilant in the event of any deterioration."

Year-round hotels were allowed to reopen on Monday but many chose to remain closed until closer to the start of the tourism season, citing low bookings.

Panos Betis, who runs a travel business and three hotels in Athens, has decided to reopen, saying it will be easier to increase capacity gradually.

"Today, we opened two rooms and tomorrow three. It's like building an anthill," Betis told AP as employees wearing face masks tidied a rooftop restaurant and cleaned a window facing the Acropolis.

"We can't compare the season to last year. We were at 95 per cent capacity. Our aim now is to hang in there till 2021," he said.

Other businesses in Greece were allowed to restart on Monday, including campsites, wedding reception services, tattoo parlors and dating agencies.

Australian Associated Press