The earthquake reached a magnitude of 5.3mww on the Richter scale and was felt in the southwest Turkish town of Bodrum, and on the southern Greek island of Kos.
It took place at a depth of 10km at 7.42am UTC (6.42am BST), the US Geological Survey (USGS) found.
Witnesses described running out of buildings, with one saying it was the strongest shake they had experienced during two weeks of smaller quakes.
One man, who was six kilometres south west from the epicentre, said: “It was very violent.”
Another, 13km west of the epicentre, said: “Powerful.”
Another witness, who was 14km from the epicentre, added: “We are very scared, we ran from the office.
“It was the most strong shake during the last two weeks.”
It was not immediately clear whether there were any injuries.
The quake struck 14km southeast of the Aegean coastal town of Bodrum, the popular resort which is thronged with Turks and foreigners on holidays during the summer months.
It is the world’s strongest earthquake in the past 24 hours, and comes just a day after a 4.6mww earthquake struck 2km from today’s epicentre.
Since July 20 there have been 20 earthquakes, including today’s, in the triangular area between Datca, Bodrum and Kos.
The strongest measured 6.6 on the Richter scale and happened almost exactly in the middle of the sea between Bodrum and Kos.
It affected a massive 250km radius, including several Greek islands and much of south eastern Turkey.
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