Relations between former allies Turkey and Israel broke down in 2010 after an Israeli naval raid on a Gaza-bound flotilla killed nine Turkish citizens.
Turkey has become the strongest critic of Israeli actions in Gaza, and reconciliation efforts between the two have repeatedly failed.
Erdogan told journalists during a flight back from Turkmenistan that "normalization with Israel" was possible if the sides can reach a compensation deal for the raid's victims and if Israel lifts a blockade against Palestinians.
Erdogan said: "There is so much the region could gain from such a normalization process.
