The coastguard said the boat, with an outboard motor, was detected at 0300 GMT off the coast of Mugla’s Bodrum district, and that it tried to flee despite repeated warnings to stop.
The boat later took in water due to adverse weather and sea conditions in the area and sank, it added.
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A coastguard helicopter and three boats were dispatched to the area for search and rescue operations, the coastguard said, adding that they had rescued 21 people so far.
The statement did not say where the boat had departed from or where it was heading.
The Aegean Sea is a frequent transit route for thousands of migrants attempting to cross from North Africa and the Middle East into Europe, particularly from Turkiye, which hosts millions of refugees from Syria, Iraq and Afghanistan.