According to the Palestinian source, Hamas has now signaled it was ready to accept the proposal.
A senior Egyptian source said that Cairo contacted Israel and the Palestinians about the new initiative.
"The plan is for a temporary ceasefire during which the border crossings will open and aid supplies to help rehabilitate the Strip would be imported," said the Palestinian source.
He emphasized that the plan postponed discussion of the divisive issues for future talks. "The matters that remain to be resolved will be deliberated in a month. We will accept the proposal, but we are waiting for an Israeli response to the offer."
Another Palestinian official said Egypt might invite Palestinian and Israeli negotiating teams to return to Cairo in 48 hours.
Egypt proposed a new initiative for an immediate ceasefire and an opening of the border crossings based on the understandings reached after Operation Pillar of Defense – with an agreement to return to negotiations within a month – according to reports from early on Monday.
Palestinian sources, including an Islamic Jihad member of the delegation in Cairo Khaled al-Batsh, said Sunday night that within a few hours Egypt would call for an immediate and ongoing ceasefire – with prior coordination from both parties.
According to the Palestinian sources, Israel would agree to a complete opening of the border crossings between Israel and Gaza for the passage of people and merchandise, allowing for the immediate start of the Strip's rehabilitation.
The Egyptian proposal includes an agreement to return to negotiations within a month to discuss difficult issues like the establishment of a seaport and an airport and the release of Palestinian security detainees.
Meanwhile, the rocket fire on southern Israel has not ceased. More than 40 rockets were fired from the Strip on Monday. The majority of the rockets were fired on the Eshkol regional council, where two people were lightly wounded by shrapnel. Iron Dome has intercepted 13 rockets since midnight.
The conflict, now in its 49th day, has killed more than 2,100 Palestinians and 68 Israelis, mostly soldiers.
AFP contributed to this report.