At the end of May, Turkey had warned of an "uncontrolled escalation" in the Black Sea region after a drone attack on a Turkish cargo ship.
Turkish officials on Tuesday said a drone attack on two civilian vessels in the Black Sea had left crew members injured.
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The foreign ministry said the ships were attacked after leaving the Russian port of Novorossiysk late on Monday and several personnel were wounded, adding that "their situation is being closely monitored."
"We are deeply concerned about the escalating conflict between Russia and Ukraine in the Black Sea, which is affecting civilian shipping despite our numerous warnings," the ministry said.
It called on all parties to "urgently implement concrete measures to ensure the safety of navigation in the Black Sea" and warned that food supplies could be affected otherwise.
According to monitoring site MarineTraffic, the two ships, identified by the ministry as Yasar and Nadezhda, sail under the Panamanian and Cameroonian flags respectively but are owned by Turkish companies.
Russia and Ukraine have been stepping up strikes on cargo vessels for several weeks.
A Turkish fishing vessel was attacked in late June in the Black Sea near the coast of Crimea, leaving one dead and four injured.
At the end of May, Turkey had warned of an "uncontrolled escalation" in the Black Sea region after a drone attack on a Turkish cargo ship.
The Ukrainian navy claimed that a Russian drone had attacked the vessel.