More than 10 days into what the Israeli military called a "limited" operation in Rafah, fighting between Israeli forces and Palestinian militants has also flared again in Gaza's north.
The Kuwaiti hospital said an overnight Israeli strike killed two people in a displacement camp in Rafah, with witnesses reporting heavy gunfire and shelling in the city's southeast and jets bombarding its eastern areas.
AFP correspondents, witnesses and medics said there were intense battles overnight in the northern Jabalia refugee camp, after the Israeli army reported on Friday "perhaps the fiercest" violence in the town in more than seven months of war.
Israel in early January said it had dismantled Hamas's command structure in northern Gaza, but the army said the Palestinian group -- whose October 7 attack sparked the ongoing war -- "was in complete control here in Jabalia until we arrived a few days ago".
The Israeli incursion into Rafah, launched despite overwhelming international opposition and as mediators were hoping for a breakthrough in stalled truce talks, has worsened an already dire humanitarian crisis, aid groups say.
With key land crossings closed or operating at limited capacity due to the fighting, some relief supplies began flowing into war-ravaged Gaza via a temporary, floating pier constructed by the United States.
The 310 pallets began moving ashore in "the first entry of humanitarian aid through the floating pier", the Israeli army said in a statement.
In the coming days, around 500 tonnes of aid are expected to be delivered to Gaza through the pier, according to US Central Command.
But UN agencies and humanitarian aid groups have warned that the so-called maritime corridor, and ongoing airdrops from planes, cannot replace far more efficient truck convoys into Gaza, where the United Nations has repeatedly warned of looming famine.
Rafah operation hampers aid
The European Union welcomed the first shipment from Cyprus to the Gaza pier, but called on Israel to "expand deliveries by land and to immediately open additional crossings".
Hamas, which rules Gaza, stressed that the floating pier "is not an alternative to opening all land crossings".
The war erupted after Hamas's unprecedented October 7 attack on Israel, which resulted in the deaths of more than 1,170 people, mostly civilians, according to an AFP tally based on Israeli official figures.
Israel's retaliatory offensive against Hamas has killed at least 35,303 people in Gaza, mostly civilians, according to data provided by the Hamas-run territory's health ministry.
Out of 252 people taken hostage from Israel during the October 7 attack, 125 remain held in Gaza including 37 the army says are dead.
The army said troops in Gaza had recovered late Thursday the bodies of three hostages who had been "murdered" on October 7.
Amid the aid shortages, the Israeli army said "dozens of Israeli civilians" set fire to a Gaza-bound aid truck in the occupied West Bank on Thursday night, in the second such attack in a week.
It came after right-wing activists ransacked at least seven aid trucks from Jordan near the Tarqumya crossing with the West Bank on Monday.
Aid groups have said the Rafah incursion has further hampered aid deliveries, with the southern city's crossing on the Egypt border -- a vital conduit for humanitarian assistance -- now shut.
Israeli Prime Minister Benjamin Netanyahu has put the onus on Egypt to reopen the crossing.
Egypt has accused Israel in turn of denying responsibility for a humanitarian crisis in Gaza and says that truck drivers and aid workers do not feel safe crossing through an Israeli checkpoint into Gaza.
West Bank commander killed
On Friday, 13 Western governments, including many traditionally supportive of Israel, appealed to it not to launch a large-scale Rafah offensive, warning it would have "catastrophic consequences" for civilians.
The looming Israeli assault has prompted nearly 640,000 of the 1.4 million people who had been sheltering in Rafah to flee to other areas, the UN humanitarian office said.
Israel has vowed to defeat remaining Hamas forces in Rafah, which it says is the last bastion of the Iran-backed group.
In northern Gaza's Beit Lahia, witnesses reported air strikes near Kamal Adwan hospital on Saturday.
The hospital's director Hussam Abu Safiya told AFP on Friday that the facility, which has received "large numbers of injured and killed" from fighting in nearby Jabalia, was running low on medical supplies and fuel to power generators.
The fuel aid that had reached the hospital was "barely enough for a few days", Abu Safiya said.
The World Health Organization has received no medical supplies in Gaza since the Rafah operation began on May 6, spokesman Tarik Jasarevic said Friday, adding that the closure of the crossing caused "a difficult situation".
On the diplomatic front, US National Security Advisor Jake Sullivan was headed to the region for weekend talks.
Sullivan will meet Saudi Crown Prince Mohammed bin Salman on Saturday and Israel's Netanyahu on Sunday, National Security Council spokesman John Kirby said.
Meanwhile Israeli forces killed a senior Palestinian militant in the occupied West Bank, where violence has flared during the war in Gaza.
Al-Quds Brigade, the armed wing of the Islamic Jihad militant group, said local commander Islam Khamayseh was killed in an Israeli air strike late Friday on Jenin refugee camp.
The Israeli military said he was responsible for a series of attacks.
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