Hamas said it was studying on Saturday the latest Israeli counterproposal regarding a potential ceasefire in Gaza, a day after media reports said a delegation from mediator Egypt arrived in Israel in a bid to jump-start stalled negotiations.

The signs of fresh truce talks come as the United Nations warned that "famine thresholds in Gaza will be breached within the next six weeks" unless massive food assistance arrives.

Aid groups say Gaza's already catastrophic humanitarian conditions would be worsened by an invasion which Israel vows to carry out against Hamas battalions that remain in Rafah, southernmost Gaza.

Rafah, on the border with Egypt, is crowded with hundreds of thousands of Palestinians displaced by nearly seven months of war between Israel and the Islamist movement.

The area is regularly bombed already. Hospital officials said strikes in Rafah and elsewhere killed more than a dozen people overnight Friday-Saturday.

Among the dead were an entire family, their relative Mohammed Yussef said.

"Nobody left: the father, the mother, a girl and two boys" were killed when their house was targeted, he said.

Elsewhere in Rafah people searched the rubble of homes that Abed al-Aziz Barhum, a young man with a thin moustache, said were "bombarded without prior warning".

He appealed to "all Arab people to support us against occupation and help us reach a ceasefire".

- Daily deaths -

Khalil al-Hayya, deputy head of Hamas's political arm in Gaza, said it had "received the official Zionist occupation response to the movement's position, which was delivered to the Egyptian and Qatari mediators on April 13".

In a statement, Hayya said Hamas "will study this proposal" before responding.

The movement has previously insisted on a permanent ceasefire, which Israel rejects.

Egypt, Qatar and the United States have been unsuccessfully trying to seal a new truce deal in Gaza ever since a one-week halt to the fighting in November saw 80 Israeli hostages exchanged for 240 Palestinians held in Israeli prisons.

A delegation from Egypt arrived in Israel on Friday hoping to revive the truce negotiations, Israeli and Egyptian media reported.

There has been "noticeable progress in bringing the views of the Egyptian and Israeli delegations closer", said Al-Qahera News, which is linked to Egyptian intelligence services.

In early April Hamas had said it was studying a proposal, after talks in Cairo, and Al-Qahera reported progress. Days later Israel and Hamas accused each other of undermining negotiations.

As talks drag on, dozens of people in Gaza die every day, according to figures from the health ministry in the Hamas-run territory.

The war began with Hamas's unprecedented October 7 attack which resulted in the deaths of about 1,170 people in Israel, mostly civilians, according to an AFP tally of Israeli official figures.

- Summit in Saudi -

Vowing to destroy Hamas, Israel's retaliatory offensive has killed at least 34,388 people in Gaza, mostly women and children, according to the health ministry.

At least 32 additional deaths are among the latest toll released Saturday, it said.

An international summit set to begin Sunday in Saudi Arabia will have a strong focus on the war, including the humanitarian situation, organisers said.

US Secretary of State Antony Blinken will be among leaders attending the World Economic Forum special meeting, organisers said.

Israel's military said Saturday its aircraft had hit more than 25 militant targets over the previous day.

Israel estimates that 129 hostages seized by militants on October 7 are still being held in Gaza, including 34 the military says are dead.

Israeli demonstrators have intensified protests for their government to reach a deal that would free the captives, accusing Prime Minister Benjamin Netanyahu of prolonging the war.

In its report on Friday, the UN's Office for the Coordination of Humanitarian Affairs (OCHA) said "the only way to halt famine" is by "massive and consistent food assistance that can be delivered freely and safely".

OCHA says rising temperatures are exacerbating Gaza's sanitation crisis, and an infant girl has reportedly died in Rafah from extreme heat.

Defence Minister Yoav Gallant said this month that Israel planned to "flood Gaza" with aid, but the OCHA report cited continued "access constraints".

A Royal Navy support ship has sailed from Cyprus to house hundreds of US army personnel building a jetty for aid sent by sea, a British defence source said on Saturday.

- Lebanon, West Bank deaths -

The main aid agency in Gaza, the UN agency for Palestine refugees (UNRWA), has been under attack and lost some of its global funding since January when Israel said several UNRWA employees were involved in the October 7 attack.

The UN immediately fired the accused staffers and began an investigation.

UN spokesman Stephane Dujarric said Friday one case has been closed "as no evidence was provided by Israel to support the allegations against the staff member".

Investigations into three others were suspended as information provided by Israel is "not sufficient", Dujarric said.

The Gaza war has led to increased violence between Israel and Iran's proxies and allies, in particular the Iran-backed militant group Hezbollah along the border with Lebanon.

Israeli strikes on southern Lebanon killed three people on Saturday, including two members of Hezbollah, the movement and official media said.

The violence has fuelled fears of all-out conflict between Hezbollah and Israel, which last went to war in 2006.

Since October 8 more than 250 Hezbollah fighters and dozens of civilians have been killed in Lebanon, according to an AFP tally.

Israel says 11 soldiers and nine civilians have been killed on its side of the border.

Violence has also soared in the Israeli-occupied West Bank where almost 500 Palestinians have been killed by Israeli forces or settlers since October 7, according to Palestinian officials.

Israeli forces shot dead two Palestinian men at a military post near the city of Jenin on Saturday, the army and Palestinian media reported.

© Agence France-Presse