This photo shows smoke billowing following Israeli bombardment in the Palestinian territory. AFP

Israeli forces pressed on with intensified attacks in the Gaza Strip's biggest southern city and a central refugee camp, after the territory's Hamas-run health ministry reported more than 21,000 people had been killed in 11 weeks of war.

The continued air strikes and the expansion of operations in the south came as the WHO warned on Wednesday that Gaza's population was in "grave peril", with France's president calling for a long-term ceasefire.

Israeli army spokesman Daniel Hagari said on Wednesday that strikes on a central refugee camp in Gaza had entered a third day, and that an additional brigade had been deployed to the southern city of Khan Yunis, the recent focus of heavy urban combat.

He also hinted at a possible "expansion of fighting in the north" along the Lebanese border, which has seen repeated exchanges of fire between Israeli troops and Hezbollah since the war in Gaza broke out.

Following a visit to the border earlier in the day, army chief Herzi Halevi said the military had "approved plans for a variety of contingencies, and we need to be prepared to strike if required".

Israel has repeatedly vowed to keep up its campaign to destroy Hamas in retaliation for its bloody October 7 attack, which left about 1,140 people dead, most of them civilians, according to an AFP tally based on Israeli figures.

An Israeli artillery unit fires near the Israel-Gaza border. Reuters

Palestinian also took around 250 hostages, 129 of whom remain in captivity, Israel says.

Israel's relentless bombardment and ground invasion have killed at least 21,110 people, mostly women and children, according to the latest toll from Gaza's Hamas-run health ministry.

The army announced the deaths of three more soldiers on Thursday morning, bring the total killed in Gaza to 167.

‘Lasting ceasefire’

Calls for an end to the hostilities continued to mount on Wednesday, with French President Emmanuel Macron emphasising in a call with Israeli Prime Minister Benjamin Netanyahu "the need to work towards a lasting ceasefire".

He also expressed his "deepest concern at the very heavy civilian toll" in Gaza, his office said in a statement, adding that France would be working with Jordan to carry out humanitarian operations in the territory "in the coming days".

Since Israel imposed a siege at the outset of the war, Gazans have faced severe shortages of food, water, fuel and medicine.

WHO chief Tedros Adhanom Ghebreyesus echoed calls for a ceasefire on Wednesday.

Palestinians carry a child injured during Israeli bombardment at Nasser Hospital in Khan Yunis on Wednesday. AFP

He pressed the international community to take "urgent steps to alleviate the grave peril facing the population of Gaza and jeopardising the ability of humanitarian workers to help people with terrible injuries, acute hunger, and at severe risk of disease".

In the same statement, the WHO said its staff had reported that "hungry people again stopped our convoys today in the hope of finding food".

‘No safe zones’

An estimated 1.9 million Gazans have been displaced, the UN says.

One of them, Iman al-Masry, recently gave birth to quadruplets in a hospital in southern Gaza after fleeing her family's home in the territory's devastated north early in the war.

The journey "affected my pregnancy", the 28-year-old said on Wednesday, and she gave birth by C-section on December 18 to two girls and two boys.

Palestinians stand over the shrouded bodies of loved ones killed during Israeli bombardment in Khan Yunis. AFP

She was quickly asked to leave the hospital to make room for other patients, but had to leave behind one son who was too fragile to go with them.

"They are very slim," she said of the infants from a cramped schoolroom turned shelter in Deir Al Balah.

"Because of the lack of... baby formula, I try to breastfeed them, but there's no nutritious food I can eat to breastfeed the three babies," she added.

Not far away, at the Al-Maghazi refugee camp, a UN-run school doubling as a shelter was hit by shelling in the night.

"They tell you there are green zones and other zones with other colours. All those are rumours, there are no safe zones in Gaza," one man told the media on Wednesday, without giving his name.