Israel has agreed pauses in its offensive in northern Gaza that will allow some civilians to flee heavy fighting, but Prime Minister Benjamin Netanyahu ruled out any broader ceasefire as a "surrender" to Hamas.

US President Joe Biden welcomed the pauses, which formalise an arrangement that has already seen tens of thousands of Palestinians flee devastation in northern Gaza, but also said there was "no possibility" of a ceasefire.

Netanyahu said Israeli troops were performing "exceptionally well" in the offensive launched after Hamas fighters poured across the border on October 7, killing 1,400 people, mostly civilians, and taking around 240 hostage.

Vowing to destroy Hamas, Israel retaliated with an aerial bombing and ground offensive that the health ministry in the Hamas-run Gaza Strip says has killed more than 10,800 people, mostly civilians and many of them children.

Netanyahu said Israel does not "seek to govern Gaza."

"We don't seek to occupy it, but we seek to give it and us a better future," he told Fox News.

Tens of thousands of civilians have streamed out of devastated northern Gaza in recent days, with men, women and children clutching meagre possessions as they emerge from the devastated warzone.

They have fled close-quarter fighting, with Hamas militants using rocket-propelled grenades against Israeli troops backed by armoured vehicles and heavy airstrikes.

The UN agency responsible for Palestinian refugees, UNRWA, said 70,000 people had travelled south on the route since November 4, most of them walking.

Almost 1.6 million people have been internally displaced since October 7, it added, more than half the area's population.

But the UN estimates hundreds of thousands of civilians remain in the fiercest battle zones in the north.

And while Biden welcomed the pauses as a "step in the right direction", there was little hope for the broader halt to fighting that aid groups and the UN say is desperately needed.

Aid groups have pleaded for a ceasefire, warning of a humanitarian "catastrophe" in Gaza, where food, water and medicine are in short supply.

"It's the first thing I think about when I wake up: how am I going to feed the children today," Amal al-Robayaa told AFP in Rafah, where she was sheltering with her husband, six children, daughter-in-law and two grandchildren at a UN school.

Oxfam France director Cecile Duflot said staff were reporting "the worst, the most tragic situation that they have ever seen" in the territory.

Overnight, fierce clashes continued, and Hamas-run local authorities accused Israel of shelling the areas of several hospitals in northern Gaza.

The Al-Shifa hospital, where an estimated 60,000 people have taken refuge, along with the Rantisi children's hospital and the Indonesian hospital all came under fire overnight, Hamas authorities said.

The bombardments caused injuries but no deaths, they added. (AFP)