Greece will resume flights to Turkey, Albania and North Macedonia, the country's Civil Aviation Authority has said.
In a related development, the weekly limit on passenger arrivals from Russia was increased from 500 to 4,000, the authority said Sunday.
Passengers from the EU and Schengen zone will also be allowed to enter the country.
Also, permanent residents from the UK, Australia, New Zealand, South Korea, Thailand, Rwanda, Singapore, UAE, Russia and Israel will be allowed to enter the country.
These passengers will, however, be required to show a negative COVID-19 test taken not more than 72 hours ago, while a seven-day quarantine will be mandatory.
Arrivals from the UK will be required to take a second test after their quarantine ends.
Apart from these few exceptions, the travel ban was extended on all domestic and international flights until March 29 and April 5, respectively, with the aim to curb the spread of COVID-19,
Passengers will be allowed to take domestic flights only if they have a health, family or business matter to attend to.
The country's health system is still under pressure with the increase in intubations related to COVID-19.
On Sunday, 674 patients were reportedly on ventilators, a rise from Saturday's 672.
The daily fatalities from the virus stood at 41.
However, the case-count on Sunday was 1,514, down from Saturday's 2,535.
The nationwide tally of infections has now reached 237,125 since the start of the pandemic, with 7,462 fatalities.