The Israeli delegation to Egyptian-mediated cease-fire negotiations was slated to continue indirect talks on Tuesday with Palestinian negotiators in Cairo, Israel Radio reported.
According to the report, Israeli officials have predicted another 72 hours will be needed to cement a long-term cease-fire deal with Hamas, in addition to the three-day truce that went into effect on Sunday.
The radio station reported that the delegation was expected to agree to ease some restrictions in Gaza, including extending fishing rights, increasing the number of materials that enter Gaza, along with Israel allowing funds to enter the Strip to be used to pay the salaries of Hamas officials.
The Israeli delegation reiterated that it was not going to give any concessions regarding Hamas' demands to open a seaport and airport in Gaza.
However, a report by the BBC quoted an official in Cairo as saying that the Palestinian delegation had waived, for now, an Israeli proposal to allow a seaport in Gaza pending the Strip be demilitarized and Hamas disarmed.
Hamas has shown no inclination to disarm in talks thus far.
An Israeli official told the Israel Radio that there had been no progress in the talks so far, as the gaps between the sides remained too vast.
A Palestinian official with knowledge of the cease-fire talks in Cairo told Reuters on Tuesday that another day was needed in Egyptian-mediated cease-fire talks before it would be evident whether a truce between Israel and Hamas would be achievable.
"So far we can't say a breakthrough has been achieved ... Twenty-four hours and we shall see whether we have an agreement," said the official speaking on condition of anonymity.
Meanwhile, a member of the Palestinian delegation to Cairo said on Tuesday that the negotiating team now in the midst of cease-fire talks, was not prepared to waive any of its demands which have been presented during the first round of the Egyptian-mediated talks.
However, the source told the al-Quds newspaper, that members of the delegation, including representatives from Hamas and the Islamic Jihad were willing to accept a gradual opening of the seaport and airport in the enclave.
That issue has proved to be the main stumbling blocks during talks, according to the source.
The delegation held a meeting Monday that lasted more than 10 hours, as the Egyptian mediators tried to bridge the gaps between the the Israelis and the Palestinians.
Reuters contributed to this report.