Israeli troops and Hamas militants engaged Tuesday in "fierce battles" in Gaza, where the dire humanitarian crisis spiralled and tearful Palestinian families scoured rubble in a desperate search for loved ones.

Footage from the Israeli military showed tanks and armoured bulldozers churning up bomb-scarred dirt tracks and troops searching shattered buildings for Hamas militants and the 240 hostages still missing.

Israel struck 300 targets during its fourth night of land operations in northern Gaza, launched after the bloodiest attack in its history when Hamas gunmen killed some 1,400 in a brutal cross-border raid, according to Israeli officials.

The army said its forces were "engaged in fierce battles with Hamas terrorists deep inside the Gaza Strip," killing dozens of militants.

Warplanes kept up a relentless barrage of strikes on Gaza, where the bombing campaign has now killed 8,525, according to the latest count given by the Hamas-run health ministry, many of them children.

The ministry later said another 50 people had died in an Israeli strike on the Jabalia refugee camp.

"We want to live like any other people in this world, to live quietly," said Ahmed al-Kahlout, a Gaza resident living near an Orthodox Cultural Centre destroyed in a strike.

"We don't know what to do. The least they can do is give us a truce, give us three hours, a temporary truce or a ceasefire," Kahlout told AFP.

Israel's Prime Minister Benjamin Netanyahu has dismissed growing international calls for a ceasefire, saying it would be "surrender" to the Hamas group he has vowed to destroy.

Hamas also released footage of battles within Gaza, including what it said was a military vehicle on fire.

None of this footage could be independently verified but AFP images showed plumes of smoke rising above Gaza and Israeli helicopters raining down rockets on the northern Gaza Strip.

- 'Stop these massacres' -

The humanitarian toll has sparked a global backlash, with aid groups and the United Nations warning time is running out for many of the territory's 2.4 million people denied access to food, water, fuel and medicine.

"Gaza has become a graveyard for thousands of children. It's a living hell for everyone else," said children's aid agency UNICEF, urging an "immediate humanitarian ceasefire".

Surgeons are conducting amputations on hospital floors without anaesthetic, and children are forced to drink salty water, said Jean-Francois Corty, vice-president of Medecins Sans Frontieres, which has 20 staff on the ground.

Israel has accused Hamas of using hospitals as military headquarters and civilians as "human shields", charges the group dismisses as "baseless" propaganda.

At a funeral in southern Gaza, tearful mourners cradled the bodies of relatives wrapped in white shrouds before burying them with their bare hands.

"We ask the world to show sympathy for the children to stop these massacres," Youssef Hijazi, the grandfather of one victim, told AFP.

As even Israel's staunchest allies voiced concern about the humanitarian crisis in southern Gaza, the UN agency for Palestinian refugees UNRWA said there was not nearly enough aid to meet the "unprecedented" needs.

"When an eight-year-old tells you that she doesn't want to die, it's hard not to feel helpless," said UN humanitarian chief Martin Griffiths.

Hisham Adwan, Gaza director of the Rafah crossing with Egypt where some aid has been allowed in, said 36 trucks had been waiting there since the previous day.

"I feel that it's extremely slow and there's disruption to UNRWA's work, and we don't know why," he said.

Israel said it is inspecting cargo to make sure weapons are not being smuggled in, and monitoring to guarantee Hamas does not seize the supplies.

- 'Great sorrow' -

The incursion scored an early victory Monday: the rescue of Private Ori Megidish, an Israeli soldier in Hamas captivity who was reunited with her family.

But there was heartbreak for relatives of another missing woman, 23-year-old German-Israeli Shani Louk, abducted from a music festival then "tortured and paraded around Gaza," according to Israel's foreign ministry.

Her remains were found Monday, with her sister Adi voicing her "great sorrow" as she shared news of her death on social media.

Other families have endured an unbearable wait for news of relatives seized by Hamas militants and thought to be held in a labyrinth of tunnels in Gaza.

Hadas Kalderon walked through the scorched homes of the Nir Oz kibbutz, near Israel's border with Gaza, where gunmen killed her mother and niece and kidnapped her 12-year-old son and 16-year-old daughter.

"I don't have any control and knowledge about army actions, I just know my children are still there in the middle of a war," said the 56-year-old.

"It's a disaster. It's really hell. There is no word to express this."

Hamas Monday released a video of what it said were three women hostages, seated against a tile wall. One urged Israel to agree to a Hamas-demanded prisoner swap.

Netanyahu dismissed the clip, the time and place of which could not be verified, as "cruel psychological propaganda".

- 'Very primitive' -

Meanwhile, in a sign that the conflict risked spiralling throughout the region, Yemen's Iran-backed Huthi rebels fired drones and missiles towards Israel and vowed to keep up attacks.

Israel's army also said it had intercepted a missile fired from the Red Sea region.

Israel's military has struck targets in Syria and traded cross-border fire with Hezbollah militants in Lebanon, whose caretaker prime minister Najib Mikati told AFP it was his "duty to prevent Lebanon from entering the war."

Anis Abla, head of Lebanon's Civil Defense Centre in Marjayoun, near the Israeli border, said they were completely unprepared for war.

"Our equipment is very primitive and there is a shortage of all tools, such as fire suits and extinguisher cylinders," he said.