Speaking just days before the submission of a U.N. report on the raid in May last year, Erdoğan said Turkey
would never forget the nine men and condemned the continuing blockade of Gaza
as "illegal and inhuman."
officially apologizes for its unlawful action which is against international laws and humanitarian values, pays compensation for the families of those who lost their lives and lifts its embargo on Gaza, normalization of relations between the two countries is unthinkable," he said.
Israel says its blockade is justified to prevent arms smugglers ferrying weapons to Hamas, the Islamist group which runs Gaza.
Erdoğan opened his speech to foreign ambassadors to the Palestinian territories in Istanbul by naming each of the men killed in the raid on the Mavi Marmara
"We have not forgotten, nor will we forget, the self-sacrifice of our brothers, their memories and the massacre they were subjected to," he said.
Turkey withdrew its ambassador to Israel after the incident in May 2010, suspended military cooperation, and closed its airspace to Israeli military aircraft.
Israel has agreed in principle to pay compensation, but says its marines acted in self-defense after an initial boarding party was attacked.
Prime Minister Benjamin Netanyahu has so far voiced only "regret" for the deaths, but Israeli officials say support for a stronger show of contrition is spreading in his government.
While some see an apology as taking responsibility, other officials have said Netanyahu had received legal advice that an apology would forestall Turkish bids to prosecute in international courts.
The United States would like its two allies to be friends again. But even if they reach closure on the Mavi Marmara incident, Turkey's sympathy for the Palestinian cause and readiness to engage Hamas will prolong tension.
"We must find a solution to the Israel-Palestinian issue on the basis of a two-state model. East Jerusalem as the capital of an independent, sovereign and viable Palestinian state is what we desire," Erdoğan said.
He also repeated his intention to visit Gaza, a trip he said would be unrelated to the apology issue.
Israel sees Jerusalem as its undivided capital and annexed the eastern part of the city after a 1967 war, a move that has not gained international recognition.
Turkey's ties with Israel hit a nadir over the Mavi Marmara incident, but they first soured after Erdoğan's criticism of the Israeli offensive in Gaza in 2009.
Erdoğan's outburst in Davos made him a hero on the Arab street, and brought Turkey newfound respect in the region.
The U.N. report into the Mavi Marmara is due to be published on July 27.