Clinton reportedly urged Netanyahu to mend ties with Turkey, The Times of Israel reported on Monday night.
Turkish and Israeli ties were badly strained in 2010 after a deadly Israeli raid of the Mavi Marmara, which was carrying humanitarian aid to impoverished Gazans in breach of an Israeli-imposed naval blockade. Nine were killed in the raid by Israeli naval commandos.
Turkey has demanded an apology, compensation for families of the victims and an end to the Gaza blockade. Israel has only expressed regret and says its soldiers acted in self-defense.
This was Clinton's first visit to the Jewish state since US-brokered peace talks between Palestinians and Israelis broke down in 2010 over Israel's refusal to halt the building of settlements on land where Palestinians hope to found a state
Clinton also met with Israeli leaders in Jerusalem, fresh from a visit to Egypt where she became the most senior US official to meet newly elected President Mohamed Mursi, from the long-banned Muslim Brotherhood.