Hamas rejected a ceasefire proposal which Egypt put forward this week, complaining it had not been a party to the discussions.
"A meeting will be held this afternoon between an official from Hamas and a representative of the Egyptian leadership," said Azzam al-Ahmad, a senior member of the Fatah movement of Palestinian president Mahmud Abbas.
Abbas himself later arrived in Cairo to join the diplomatic efforts to end the Gaza conflict in which 213 Palestinians have been killed since July 8.
Israel initially accepted the Egyptian initiative, but later intensified its air strikes aimed at stamping out rocket fire by Gaza militants following Hamas's rejection of the plan.
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Ahmad's remarks came as Middle East peace Quartet envoy Tony Blair held talks with Egyptian President Abdel Fattah al-Sisi and Foreign Minister Sameh Shoukri, on his second visit to Cairo in a week to discuss the Gaza conflict.
Blair said Egypt's initiative was designed "to allow all the issues that are at the heart of this problem .. To be dealt with in a thorough and proper way."
"But the purpose of this initiative is to allow people to come and discuss those issues, but in the meantime for the violence to stop and for the lives of the innocent to be saved," Blair said at a joint news conference with Shoukri.
Shoukri said Egypt's proposal aimed at "stopping military actions in order to address the situation in Gaza in the medium and long terms, and to give an opportunity to resume the peace process.