Egypt is due to host Friday a high-level Hamas delegation for talks aimed at putting an end to the nearly 12-week Gaza war.
The Cairo meeting comes as fighting rages in the besieged Palestinian territory's south and centre.
Israeli shelling near a southern Gaza hospital has killed 41 people over the past two days, the Palestinian Red Crescent said on Thursday.
The casualties in repeated Israeli strikes near the al-Amal hospital in Khan Younis include "displaced persons seeking shelter", the Red Crescent said in a statement.
The UN humanitarian office said an estimated 100,000 more displaced people had arrived in the already-teeming southern border city of Rafah in recent days following the intensification of fighting around Deir al-Balah and Khan Younis.
The Israeli military on Friday said its forces "are extending operation in Khan Younis" and had "eliminated dozens of terrorists" across Gaza over the past 24 hours.
AFPTV footage showed smoke billowing over Rafah, near Egypt, following fresh strikes early on Friday.
The health ministry in Gaza said on Thursday Israeli shelling had killed 20 people, most of them women and children, at the Shaboura camp in Rafah.
Israel's relentless aerial bombardment and ground invasion in Gaza have killed at least 21,320 people, mostly women and children, according to the health ministry. The Israeli army says 168 of its soldiers have been killed inside Gaza.
Sources close to Hamas say Egypt's three-stage plan provides for renewable ceasefires, a staggered release of hostages in exchange for Palestinians held by Israel, and ultimately an end to the war.
Around 250 hostages were also taken during the 7 October attack by Hamas and other Palestinian militants, with more than half of those taken currently remaining captive.
The attack also killed about 1,140 people, mostly civilians, according to an AFP tally based on Israeli figures.
A Hamas official, speaking on condition of anonymity, told AFP the delegation in Cairo would "give the response of the Palestinian factions, including several observations" regarding the Egyptian proposal, recently put to officials from Hamas and another Gaza armed group, Islamic Jihad.
Hamas would also seek "guarantees for a complete Israeli military withdrawal" from Gaza, the official said.
The proposal provides for a Palestinian government of technocrats after talks involving "all Palestinian factions", which would be responsible for governing and rebuilding in post-war Gaza.
Diaa Rashwan, who heads Egypt's State Information Services, said the plan was "intended to bring together the views of all parties concerned, with the aim of ending the shedding of Palestinian blood".
In Israel, a rally on Thursday calling for a ceasefire drew hundreds of protesters to a central square in the coastal city of Tel Aviv.
"Israelis, Palestinians, Muslims, Jews, Christians – this is everybody's home," said protester Itay Eyal, a 51-year-old teacher.
"The only solution is to recognise that both peoples are entitled to life, freedom, sovereignty and dignity."
The bloodiest ever Gaza war has also sharply heightened tensions between Israel and its long-time arch foe Iran, which supports armed groups across the Middle East.
Israel has traded heavy cross-border fire with Iran-backed Hezbollah since the Gaza war erupted, and on Friday said its military had struck "Hezbollah infrastructure in southern Lebanon" after reporting rocket fire from there.