Delegations led by powerful Turkish foreign ministry undersecretary Feridun Sinirlioglu and Joseph Ciechanover, an advisor to Israeli Prime Minister Benjamin Netanyahu, and Israeli National Security Advisor Jacob Nagel started talks in Geneva late on Wednesday, the Turkish NTV television channel reported.
Israeli officials declined to comment and the Turkish foreign ministry said it would neither confirm nor deny the talks.
NATO member Turkey was a key regional ally of Israel until the two countries fell out in 2010 over the deadly storming by Israeli commandos of a Turkish aid ship, the Mavi Marmara, bound for Gaza.
Turkey's President Recep Tayyip Erdogan further raised hackles in Israel with his sometimes inflammatory rhetoric towards the Jewish state.
But the atmosphere was transformed following the revelation in December that the two sides had met that month in secret talks to seek a rapprochement.
The Geneva talks are the first since the December meeting, NTV said.
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Turkey has repeatedly made clear three conditions for a normalisation: the lifting of the Gaza blockade, compensation for the Mavi Marmara victims and an apology for the incident.
Israel has already apologised and negotiations appear to have made progress on compensation, leaving the blockade on the Hamas-ruled Gaza Strip the main hurdle.
Omer Celik, the spokesman of the ruling Justice and Development Party (AKP), said Thursday the negotiations were "going well", without confirming the new Geneva talks.
But he emphasised the importance of Israel fulfilling all the conditions for a deal to be reached. "Details are very important in these negotiations," he told reporters in Ankara.
Meanwhile, Israel's Haaretz daily reported Thursday that Israeli Defence Minister Moshe Yaalon is demanding that any reconciliation agreement with Turkey includes the return of the bodies of two Israeli soldiers declared killed in the Gaza war in the summer of 2014.
According to Haaretz, Yaalon has adopted a hardline stance in the face of the reconciliation efforts, contributing to a hesitation on the part of Netanyahu.
Analysts have suggested that Turkey's desire for a rapprochement has been accelerated by the need for Ankara to make up for the crisis in its ties with Moscow after the shooting down of a Russian warplane, with a particular eye on Israel's gas reserves.