The 3,300-dwt Fort Azov (built 1970) went down on Thursday night while anchored a mile from Sinop after developing a list, local media said.
The vessel had left Varna in Bulgaria on 17 February.
Its master requested aid from the coast guard at 2100 hours local time that night and a rescue boat reached the vessel within three hours.
Adverse weather made the transfer of crew too difficult, but by Wednesday morning the captain believed the ship could sink at any moment.
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