Turkey says it intends to rebuild its relations with Israel, which have become severely strained over the past year.
Foreign minister Ahmet Davutoglu says he wants reconciliation.
Israeli troops killed eight Turks and a Turkish-US national when a Turkish aid ship was stopped at sea en route to Gaza on 31 May.
Mr Davutoglu reiterated that Israel must apologise for the deaths, which led Turkey to withdraw its ambassador.
Israel, which insists the commandos fired in self-defence, said it was also seeking better relations with Ankara.
The BBC reports the two nations have had 15 years of good relations, including a number of military and trade pacts, and have held talks in Geneva recently to try to restore ties.
But the talks foundered, reportedly because Israel refused to apologise for the incident on the high seas.
Meanwhile, crowds have welcomed the ship, Mavi Marmara, back to Istanbul.
It was part of a flotilla trying to break the Israeli naval blockade of the Gaza Strip, which has been in force since 2007.
Israel still maintains a complete air and naval blockade aimed at stopping weapons from being smuggled into Gaza.
