The proposal, made last week, follows an escalation in violence after Israel resumed air and ground operations against Hamas militants on March 18, effectively ending a two-month period of relative calm after 15 months of war.
Gaza Strip health officials said Israeli air strikes and shelling have killed nearly 700 Palestinians since then, including at least 400 women and children.
Among those killed on Monday were two local journalists Mohammad Mansour and Hussam Shabat, medics said.
The Palestinian Journalist Syndicate said at least 206 journalists have been killed by Israeli fire in the Gaza Strip since early October 2023, when the conflict erupted.
There was no immediate Israeli comment.
Islamist group Hamas said several of its senior political and security officials had also been killed.
The Egyptian plan calls for Hamas to release five Israeli hostages each week, with Israel implementing the second phase of the ceasefire after the first week, two security sources said.
Hamas is still holding 59 hostages, with 24 of them thought to be still alive, among the more than 250 it seized in its October 7, 2023 cross-border attack on Israel.
Most of the rest have been freed in periodic negotiated exchanges.
Both the United States government and Hamas have agreed to the proposal, the security sources said, but Israel has not yet responded.
A Hamas representative did not confirm the proposed offer but told Reuters that "several proposals are being discussed with the mediators to bridge the gap and to resume negotiations to reach common ground that would pave the way to start the second phase of the agreement".
The sources said the Egyptian proposal includes a timeline for a full Israeli military withdrawal from the Gaza Strip, backed by US guarantees, in exchange for the release of remaining hostages.
Hamas has accused Israel of breaking the terms of the January ceasefire agreement but has said it is willing to negotiate a renewed truce and was studying proposals from US President Donald Trump's special envoy Steve Witkoff.
Israel says it resumed its military operations to force Hamas to release the remaining hostages it is holding.
It says it does its best to reduce harm to civilians and has questioned the death toll provided by health authorities in the Hamas-run enclave.
Palestinian officials on Sunday put the number of dead from nearly 18 months of conflict at more than 50,000.
Israel launched its offensive in the Gaza Strip after Hamas fighters stormed southern Israel on October 7, 2023, killing 1200 people, mostly civilians, according to Israeli tallies.
In the city of Rafah, the municipality said thousands of people were stuck inside the Tel al-Sultan district where some Israeli military forces had entered, with families trapped among the ruins, with no water, food or medicine.
The Palestinian Civil Emergency Service said 50,000 residents remained cornered in Rafah, which abuts the border with Egypt.
The Israeli military said troops had encircled Tel al-Sultan to dismantle "terror infrastructure sites and eliminate terrorists in the area".
UNRWA, the United Nations Palestinian relief agency for Palestinians, said 124,000 people have been displaced in the Gaza Strip in recent days.
"Families carry what little they have with no shelter, no safety, and nowhere left to go. The Israeli authorities have cut off all aid. Food is scarce and prices are soaring. This is a humanitarian catastrophe. The siege must end," UNRWA said on X.
