Many shops, offices and businesses in Athens remained closed for the day, with only a handful of pedestrians walking the streets of the city centre as cars needed snow chains.
Police said more than 200 car accidents had been reported in the past 36 hours due to icy roads and the fire brigade had received more than 170 calls for the transfer of patients to and from hospitals for regular treatment.
In Turkey, snowfall and subzero temperatures have forced the closure of schools and universities across much of the country.
The Bosphorus strait has been closed to transit shipping in the north-south direction since Sunday morning, the coast guard said.
The strait is the only navigable waterway between the oil-shipping ports on the Black Sea and the Aegean.
"Like Siberia," read the headline in Turkey's Takvim newspaper, above pictures of snow ploughs, heavily wrapped-up pedestrians and a grounded airplane.
With some major roads closed, hundreds of motorists were stranded around the country.
Thousands of villages were cut off and at least two people froze to death on Sunday and Monday, Turkish media reported.
The capital Ankara has witnessed 355 traffic accidents over the past 24 hours and nearly 30 people have been injured, the private broadcaster NTV said.
Temperatures in Ankara were expected to remain below zero until Wednesday.
In Istanbul, Turkey's largest city, the bad weather caused more than 500 traffic accidents.
In mountainous eastern Turkey, night temperatures plunged to minus 20 degrees C, and parts of Turkey's Mediterranean coast, normally clement in the winter months, experienced rare snowfall.
In Greece, snow also made a rare appearance on the islands of Crete and Mykonos early on Monday, while at least 100 villages on the islands of Evia and Crete as well as in central Greece were cut off.
Civil defence authorities were on alert, with problems with utility services reported across the country.