Officials said twelve people were killed in coastal areas in Turkey's west, while two teenagers died on the Greek island of Samos after a wall collapsed on them.
In Turkey, at least 20 buildings in the city of Izmir alone were destroyed, Mayor Tunc Soyer told CNN Turk. Images showed vehicles crushed under the buildings and people digging through the rubble in search of survivors.
More than 419 people have been injured in Turkey, the country's disaster agency said, dozens of them saved by rescue teams using diggers and helicopters to search for survivors. Search and rescue operations continue in 17 buildings, the agency added.
TV footage showed water flooding through the streets of Cesme and Seferihisarin in parts of Turkey's wider Izmir province, as well as on the Greek island of Samos, in what officials described as a "mini tsunami." No tsunami warnings were issued.
Idil Gungor, who works as a journalist and runs a guesthouse in the Turkish town of Siğacik in Izmir province, said that the area was damaged more by the force of the water than the quake itself.
The United States Geological Survey (USGS) measured the tremor's magnitude at 7.0, while Turkish authorities said it was 6.6. The quake struck 14 kilometers (8.7 miles) northeast of the town of Néon Karlovásion on Samos, the USGS reported, at 1:51 pm Greek time (7:51a.m. ET).
But it hit at a relatively shallow depth of 10 kilometers, the USGS reported, making its impact powerfully felt at ground level around the epicenter.
Authorities in both countries have reported dozens of aftershocks. Izmir Governor Yavuz Selim Köşger called on residents to stay off the roads and refrain from using mobile phones unnecessarily so that emergency vehicles could reach affected areas and response teams could communicate effectively.
In Greece, Samos Deputy Mayor Giorgos Dionisiou told Greek media that some old buildings had collapsed on the island.
People have been told by Greek authorities to stay away from the shore and buildings, and to be on alert for high waves as aftershocks continue.
Greek Prime Minister Kyriakos Mitsotakis said on Twitter he had spoken to Turkish President Recep Tayyip Erdogan. Tensions between the two nations have flared recently over energy claims in the eastern Mediterranean.
"I just called President @RTErdogan to offer my condolences for the tragic loss of life from the earthquake that struck both our countries. Whatever our differences, these are times when our people need to stand together," Mitsotakis wrote.