Chief Israeli negotiator Amos Gilad is expected in Cairo for high-level talks with Egyptian authorities Thursday, Egypt's official MENA news agency reported.
His visit comes after talks between Hamas and Egypt ended on Wednesday without a final agreement on a truce, reported dpa.
Egypt had originally set Thursday as the deadline for Hamas to agree to a truce in Gaza, but on Thursday morning an unnamed Egyptian official told MENA that Hamas would give its response on Saturday.
The official said that Hamas was seeking clarification from the Israelis on questions regarding the opening of border crossings into the Gaza Strip.
Moussa Abu Marzouq, Hamas' deputy political leader, on Wednesday night told the Arabic satellite news channel al-Jazeera that Israel had offered to open the border crossing at 70 per cent capacity.
In remarks published in Cairo's flagship government daily al-Ahram Thursday, Mohammed Nasr, a senior member of the Hamas delegation, said Hamas was seeking clarifications on the administration of Gaza's borders.
Specifically, he said Hamas wanted Israeli officials to clarify what materials would be banned on the grounds that they could be used to build rockets.
"Will this be subject to Israeli whims?" Nasr asked.
Israeli officials have repeatedly said they want guarantees that weapons-smuggling into the Gaza Strip will stop. Hamas has repeatedly said that it wants guarantees that the blockade on Gaza will be lifted.