Israel's Prime Minister Benjamin Netanyahu has reportedly apologised to his Turkish counterpart for the deaths of Turkish citizens in the Gaza flotilla incident.
Mr Netanyahu is said to have called Recep Tayyip Erdoğan shortly before US president Barack Obama left Israel on Friday afternoon.
The Israeli and Turkish leaders have not spoken for more than two years following the Mavi Marmara incident in May 2010. Nine Turkish anti-Israel activists were killed when Israeli forces stormed the ship.
Reuters reported a US official saying that Mr Erdogan had accepted Mr Netanyahu's apology and agreed that the countries should normalise relations. It is thought Israel will compensate the families of those who died.
Mr Obama released a statement welcoming the call. He said: "The United States deeply values our close partnerships with both Turkey and Israel, and we attach great importance to the restoration of positive relations between them in order to advance regional peace and security.
"I am hopeful that today's exchange between the two leaders will enable them to engage in deeper cooperation on this and a range of other challenges and opportunities."
Turkey had long demanded an apology for the flotilla deaths, compensation for bereaved families, and an end to the blockade of Gaza.
The affair had plunged relations between the two countries to their lowest point. In September 2011, Turkey expelled the Israeli ambassador and formally downgraded diplomatic ties.
Public anger in Israel led to widespread cancellations of summer holidays in Turkish resorts.
Last summer it was reported that British Prime Minister David Cameron had passed on a personal message from Mr Netanyahu to Mr Erdogan when the latter came to London to attend the Olympic Opening Ceremony.