The Turkish president did not reveal further details of the timing of the visit in August, but said a potential prisoner swap agreement between Russia and Ukraine would be among the issues discussed.
“I hope we will get a result from this soon,” Mr Erdogan told reporters in the early hours of Saturday morning.
“If we make some phone calls before [the face-to-face meeting], we will discuss it on the call as well,” he added.
Putin and Mr Erdogan previously held talks in Kazakhstan in October last year.
Mr Zelenskyy said he would wait for the outcome of any prisoner exchange deal before commenting, but added: “We are working on the return of our captives, political prisoners, Crimean Tatars.
“Our partners have all the lists. We are really working on this.”
But despite the tensions, and Turkey’s membership of NATO, Mr Erdogan has strived to maintain relations with both Ukraine and Russia during the conflict.
Turkey has not joined in with Western economic sanctions, but has supplied arms to Ukraine and rejected Russian attempts to annex its territory.
During the press conference, Mr Erdogan also backed Ukraine’s bid to join NATO once the war was over, and said he would continue efforts to try to negotiate an end to the conflict.
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Putin makes surprise public appearance
Putin’s visit to Turkey has not been confirmed by the Kremlin.
But spokesman Dmitry Peskov, speaking to reporters before Saturday’s press conference in Istanbul, said: “As for forthcoming contacts between Putin and Erdogan, we do not rule them out in the foreseeable future.”