This would be the first meeting between such senior Turkish and Israeli officials since May's deadly Navy raid on a Gaza-bound flotilla.
The two leaders are expected to sit on the same stage for the first time as part of a panel. Peres is scheduled to address the General Assembly on Monday and attend the panel together with Gul and Palestinian President Mahmoud Abbas the next day.
The last time Peres sat on the same stage with a senior Turkish official was at the World Economic Forum in Davos after the Israeli operation in Gaza, when Turkish Prime Minister Recep Tayyip Erdogan stormed off after a heated exchange of words.
This time, Israeli officials hope the opportunity to meet on the sidelines of the General Assembly event will help improve the relations between the two countries.
An official source, who asked to remain anonymous, told the Zaman paper President Gul had noted that "foreign ministers are allowed to meet with elements from enemy states even in the battlefield." He was addressing Turkish Foreign Minister Ahmet Davutoglu's meeting with Industry, Trade and Labor Minister Binyamin Ben-Eliezer in Brussels after the flotilla incident in a bid to ease the tensions between the two countries.
Gul to demand apology
According to the report, during the meeting Gul is expected to stress Turkey's conditions for improving the relations and to clarify that there would be no normalization between the two countries without an Israeli apology for what Ankara has defined as "an attack" on the flotilla.
Gul is also expected to demand that Israel compensate the families of the nine Turkish civilians killed during the violent incident onboard the Marmara ship.
He is likely to recommend that Jerusalem submit its apology through to the international commission of inquiry into the flotilla incident appointed by UN Secretary-General Ban Ki-moon.
Representatives of the 192 member states are expected to attend the UN General Assembly meeting next week for discussions on various issues, including ways to fight world poverty.
Gul is slated to head the Turkish delegation, although his doctors have warned that the trip may endanger his health.
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