Talks to reach a Gaza truce were expected to resume Sunday after officials from the Hamas Islamist organisation and Israel publicly disagreed over demands to end their seven-month war.
While mediation took place in Egypt, the head of the UN's World Food Programme said "there is famine" in northern Gaza, and appealed for a ceasefire.
The war's impact has been increasingly felt around the world as pro-Palestinian university students from Australia to Mexico and Europe follow the example of protest encampments set up in the United States.
Gaza's bloodiest-ever war began following Hamas's unprecedented 7 October attack on Israel that resulted in the deaths of more than 1,170 people, mostly civilians, according to an AFP tally of Israeli official figures.
Vowing to destroy Hamas, Israel's retaliatory offensive has killed at least 34,654 people in Gaza, mostly women and children, according to the Hamas-run territory's health ministry.
An AFP correspondent and witnesses on Sunday reported shelling and gunfire in the Gaza City area, helicopter fire in central and southern Gaza, and a missile strike on a house in the Rafah area.
The Palestinian civilian toll has strained ties between Israel and its main military supplier and ally the United States.
Nonetheless, Washington's Secretary of State Antony Blinken said "the only thing standing between the people of Gaza and a ceasefire is Hamas."
Negotiators have proposed a 40-day pause in the fighting and an exchange of hostages for Palestinian prisoners, according to details released by Britain.
It would be the first such truce since a week-long ceasefire saw 105 hostages released last November in exchange for Palestinians held by Israel.
Qatari, Egyptian and US mediators met a Hamas delegation in Cairo on Saturday and a senior Hamas source close to the negotiations told AFP there would be "a new round" of talks on Sunday.
After "no developments" in the first round, a senior Hamas official separately insisted late Saturday that the group would "not agree under any circumstances" to a truce that did not explicitly include a complete end to the war, including Israel's withdrawal from Gaza.
The official, who was not authorised to speak publicly, condemned Israeli efforts to secure a hostage-release deal "without linking it to ending the aggression on Gaza".
He accused Israel's Prime Minister Benjamin Netanyahu of "personally hindering" truce efforts due to "personal interests".
A top Israeli official, also not authorised to comment, said on Saturday that Hamas was "thwarting the possibility of reaching an agreement" by refusing to give up its demand for an end to the war.
A source with knowledge of the negotiations had on Wednesday said Israel's proposal contained "real concessions" including a period of "sustainable calm", but the source said Israel's withdrawal from Gaza remained a likely point of contention.
The Israeli official on Saturday, however, told AFP in Jerusalem that Israel has not agreed to any guarantees that the war will end.
Previous negotiations stalled in part due to Hamas's demand for a lasting ceasefire and Netanyahu's vows to crush the group's remaining fighters in the far-southern city of Rafah, where half of Gaza's population is sheltering.
Israel has yet to send a delegation to Cairo. The Israeli official said it would do so only if there were "positive movement" on the proposed framework.
"Tough and long negotiations are expected for an actual deal," the official added.
Netanyahu has vowed to invade Rafah regardless of whether a truce is reached, and despite concerns from the United States, other countries and aid groups.
Blinken on Friday said Israel has not presented a plan to protect civilians. Without it, "we can't support a major military operation going into Rafah because the damage it would do is beyond what's acceptable," Blinken said.
Netanyahu on Thursday vowed to "do what is necessary to win and overcome our enemy, including in Rafah."
At the start of the war, Israeli Defence Minister Yoav Gallant said his country would impose a "complete siege" blocking food, water and other supplies.
Continuous appeals from aid groups, the United Nations and world leaders for greater access have led to some improvements.
Israel said the Erez crossing in north Gaza has reopened for aid entry, and assistance has arrived via the Israeli port of Ashdod.
On Friday the UN humanitarian agency OCHA said there has been recently observed "incremental progress in access to food, water, and sanitation facilities."
But Cindy McCain, executive director of the World Food Programme, said in an interview excerpt published Friday: "There is famine, full-blown famine in the north and it's moving its way south."
She appealed for a ceasefire and unfettered, safe access to the territory.
West Bank deaths.
Protesters in Israel have accused Netanyahu of seeking to prolong the war.
Netanyahu, on trial for corruption charges he denies, leads a coalition which includes religious and ultra-nationalist parties.
In their October attack the militants seized hostages, of whom 128 remain in Gaza, including 35 who the military says are dead.
On Sunday the Hostages and Missing Families Forum appealed directly to Netanyahu in a statement, telling him to "disregard all political pressure."
The group added: "History will not forgive you if you miss this opportunity" to bring home the hostages.
Thousands of Israelis again rallied in Tel Aviv late Saturday demanding a deal to free the remaining captives. They waved Israeli flags and placards calling on the government to "Bring them Home!"
Michael Levy, whose brother Or Levy is among the hostages, said he tries not to think too much about a potential truce deal "until this is real."
"We hear those rumours about an upcoming deal pretty much since 8 October," he said.
The war in Gaza has also triggered worsening violence in the Israeli-occupied West Bank. Israel's army said on Saturday its troops killed five Palestinian "terrorists" during a 12-hour operation near Tulkarem.
Hamas's armed wing reported the death of three fighters, including its Tulkarem chief Alaa Adib.