RAFAH, Palestinian Territories, June 2, 2024 (BSS/AFP) - Israel bombarded the Gaza Strip and battled Hamas Sunday as mediators called on both sides to agree to a truce and hostage release deal outlined by US President Joe Biden.

Since Biden spoke at the White House on Friday, Prime Minister Benjamin Netanyahu has insisted Israel will pursue the war, now nearing its ninth month, until it has destroyed Hamas and freed the captives.

Palestinian group Hamas, meanwhile, has said it "views positively" what Biden described as an Israeli proposal.

Netanyahu, a hawkish political veteran leading a fragile right-wing coalition government, is under intense domestic pressure from two sides.

Protesters backing an immediate hostage release, who rallied again Saturday in Tel Aviv, want him to strike a truce deal, but his far-right allies are threatening to bring down the government if he does.

Opposition leader Yair Lapid has offered Netanyahu political support if the government secures a deal.

Fighting rocked Gaza overnight and Sunday, with Israel's military reporting air strikes and ground combat.

Across Gaza, the military said Sunday it had struck "30 terror targets" over the past day, including "weapons storage facilities" and Hamas.

Netanyahu said Saturday that "Israel's conditions for ending the war have not changed: the destruction of Hamas's military and governing capabilities, the freeing of all hostages and ensuring that Gaza no longer poses a threat to Israel".

Mediators the United States, Qatar and Egypt later said they "call on both Hamas and Israel to finalise the agreement embodying the principles outlined by President Joe Biden".

White House National Security Council spokesman John Kirby told ABC News Sunday that "we have every expectation that if Hamas agrees to the proposal, as was transmitted to them -- an Israeli proposal -- that Israel would say yes."

"We're waiting for an official response from Hamas," he added.

- Political pressure -

The Gaza war was sparked by Hamas's unprecedented October 7 attack, which resulted in the deaths of 1,189 people, mostly civilians, according to an AFP tally based on Israeli official figures.

Hamas also took 252 hostages, 121 of whom remain in Gaza, including 37 the army says are dead.

Israel's retaliatory bombardments and ground offensive have killed at least 36,439 people in Gaza, mostly civilians, according to the Hamas-run territory's health ministry.

According to Biden, Israel's three-stage offer would begin with a six-week phase that would see Israeli forces withdraw from all populated areas of Gaza and an initial hostage-prisoner exchange.

Israel and the Palestinians would then negotiate for a lasting ceasefire, with the truce to continue as long as talks are ongoing, Biden said, adding it was "time for this war to end".

Netanyahu took issue with Biden's presentation, insisting that according to the "exact outline proposed by Israel" the transition from one stage to the next was "conditional" and crafted to allow it to maintain its war aims.

Finance Minister Bezalel Smotrich and National Security Minister Itamar Ben Gvir, leaders of the two extreme-right parties in parliament, warned they would leave the government if it endorsed the truce proposal -- potentially costing Netanyahu's coalition its majority.

Smotrich said on X he opposed the "wholesale release of terrorists" in a prisoner swap, adding: "We demand the continuation of the war until Hamas is destroyed and all hostages return."

Lapid, a centrist former premier, said that the government "cannot ignore Biden's important speech" and vowed to back Netanyahu if his far-right coalition partners quit.

"I remind Netanyahu that he has our safety net for a hostage deal," Lapid said on X.

Israeli Defence Minister Yoav Gallant said Sunday the defence establishment was "assessing a governing alternative" to Hamas for post-war Gaza.
- Helicopter strikes -

Heavy fighting has flared in Gaza's far-southern Rafah city, where Israel sent tanks and troops in early May, ignoring concerns for displaced civilians there.

The UN agency for Palestinian refugees, UNRWA, said Sunday all 36 of its shelters in Rafah "are now empty", after at least a million people have fled the city.

"The humanitarian space continues to shrink", UNRWA said, adding that about 1.7 million people were now sheltering in southern Gaza's main city of Khan Yunis and in central areas.

Witnesses said Israeli Apache attack helicopters struck central Rafah Sunday, while a jet fired a missile at a house in the western Tal al-Sultan district and artillery targeted the southern Brazil neighbourhood.

There were also clashes in the city centre and drone attacks, witnesses told AFP.

The Palestinian Red Crescent said it was "very difficult" to access Rafah because of the Israeli bombardment.

In the besieged territory's north, Israeli helicopters fired at Gaza City's Zeitun and Sabra areas, and an air strike hit a house in the city's east, AFP reporters said.

A hospital medic said three people were killed when an air strike hit a family apartment in Gaza City's Daraj district.

And in central Gaza, shelling hit areas of Deir al-Balah and the Bureij and Nuseirat refugee camps, witnesses said.

Israel's seizure last month of the Rafah crossing has further slowed sporadic aid deliveries for Gaza's 2.4 million people and effectively closed its main exit point on the Egyptian border.

Egyptian state-linked Al-Qahera News said a Sunday meeting in Cairo with Israeli and US officials to discuss reopening the crossing had ended, without saying whether an agreement was reached.

Quoting a senior official, Al-Qahera said Egypt reiterated its demand that "Israel withdraw from the Palestinian side of the Rafah crossing so it can resume operations".

Cairo refuses to coordinate with Israel humanitarian deliveries through Rafah, but has agreed to send some aid via Israel's Kerem Shalom crossing.