Akar and the air force, army and navy chiefs landed by helicopter on the Oruc Reis off the Aegean Sea, the defence ministry said in a statement, without specifying the exact location.
Turkey deployed the Oruc Reis and warships to the disputed waters last year and has extended its mission several times despite repeated calls to stop by Greece and the European Union.
Turkey says Greece is using its islands to lay claim to huge swathes of the Aegean and Mediterranean Seas and came under EU sanctions in December.
President Recep Tayyip Erdogan vowed Saturday that Turkey would not give up on its rights in the eastern Mediterranean, in a live video conference.
Ankara first began massive naval drills called the Blue Homeland in 2019 to test its fighting capabilities in the Aegean and the Mediterranean but had to cancel them last year because of the coronavirus pandemic.
This year's drills, between February 25 and March 7, are being carried out "stronger and more organised", Erdogan said.
"We have the opportunity to see our heroic army's knowledge and capabilities," he said.
"We are not eyeing any country's land, sea or sovereignty. We're only trying to protect our homeland and rights," he said, adding Ankara would do so "at all costs."
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