The meeting comes almost a month after both sides agreed to halt a devastating 50-day war in Gaza and hold subsequent negotiations on key Palestinian demands for a lasting ceasefire.
It was almost derailed earlier today after Palestinian negotiaters threatened to pull out over the Israel military operation in the West Bank city of Hebron in which the two suspects were killed.
Israel says the two, Amer Abu Eisha and Marwan Qawasmeh, were behind the murder of the teenagers, which led to weeks of simmering violence and culminated in the war between Israel and Hamas militants in Gaza.
Rishq condemned the "assassination," and the meeting was delayed by two hours, but the official Egyptian MENA news agency later reported that the meeting had begun.
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The negotiators are expected to set a timetable for further talks after the Muslim Eid al-Adha holiday in the first week of October, a Palestinian official said.
An August 26 ended the Gaza conflict, which killed more than 2,140 Palestinians, most of them civilians, and 73 on the Israeli side, mostly soldiers, with an agreement to start negotiations in a month on unresolved issues.
Hamas, an Islamist militant movement designated as a terrorist group by the United States, Israel and the European Union, will also hold separate negotiations in Cairo with the Fatah faction of Palestinian president Mahmud Abbas.
The factions formed a unity government in June to end a seven-year rift during which Hamas seized control of Gaza, and the Islamists remain the de facto rulers of the coastal enclave.
The talks will focus on the transfer of power in Gaza to the national unity government and on security there, a member of the Fatah delegation said.