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Greece will place all incoming travellers in quarantine for two weeks to limit the spread of the coronavirus, a government official said Monday.

"Any who enter Greece will be placed under obligatory (quarantine) for 14 days," acting government spokeswoman Aristotelia Peloni told reporters, saying the measure will be applied "from now on... regardless of nationality".

Those who do not abide by the regulations will face fines, she added.

The spokesperson did not clarify if this would also affect transit and transfer flights. An aviation industry source told AFP such travellers were "unlikely" to be affected, pending further government clarifications.

Greece has progressively tightened restrictions on trade and public gatherings as the national death toll from the virus rose to four at the weekend.

The health ministry's spokesman on the virus Sotiris Tsiodras on Monday announced 21 new cases, raising the national total to 352.

Nine people are in intensive care, and ten have been discharged, Tsiodras said.

Peloni said most retail outlets would also be shuttered as of Wednesday, with the exception of pharmacies, supermarkets, petrol stations and banks.

Later Monday, the Holy Synod, governing body of the Orthodox Church of Greece, said weddings and baptisms would be held without guests, and funeral services would be limited to close family members of the deceased.

But the Synod stopped short of closing churches or suspending Holy Communion, a measure critics have been demanding for days.

Greece has already closed its borders with Albania and North Macedonia except to returning Greek nationals and residents, stopped flights to and from Spain and suspended passenger ship services to Italy.

Cruise ships will also no longer be allowed to dock at Greek ports.

Greece also closed pay-to-enter beaches from Sunday—thwarting attempts by Greeks hoping to enjoy the fine weather there after bars and restaurants were closed.

Seasonal hotels are being closed until April 30.

The government had already shut down schools, universities, courts, cinemas and gyms last week.

Police said they have arrested dozens of people for failing to observe the new rules since Thursday.