A Palestinian sits among destruction from the Israeli bombardment in the Nusseirat refugee camp in Gaza. AP

Israel kept up its heavy assault on the "encircled" Gazan city of Khan Yunis following an outpouring of grief over the army's deadliest single day since ground operations in the territory began.

Israel has carried out a relentless offensive that has killed at least 25,490 people in Gaza, around 70 per cent of them women and children, according to the health ministry in the Hamas-run territory.

As the fighting raged, the UN humanitarian agency OCHA reported that Israeli forces on Tuesday had issued fresh evacuation orders for a section of Khan Yunis housing an estimated half a million residents and displaced people.

The orders came as the World Food Programme warned that Gazans were facing "catastrophic food insecurity", and as the UN chief took Israel to task over its rejection of a two-state solution — seen by ally the United States as the only path to a durable peace.

Twenty-four Israeli troops were killed on Monday, 21 of them reservists slain "when a squad of terrorists surprised the force" with rocket-propelled grenade fire, military spokesman Daniel Hagari said Tuesday.

"The price of the war is heavy and painful," he added.

Mourners pray next to the dead bodies killed in an Israeli strike in Rafah, Gaza Strip. Reuters

Mourners filed into funerals for the reservists on Tuesday, including some with no connection to the deceased.

Israela Oron, of the Ben-Gurion University of the Negev, said the mounting soldier deaths — now at 221 — would prompt the public to "demand clear answers about the purpose and the goal of this operation in Gaza".

Prime Minister Benjamin Netanyahu said an investigation had been launched into the "disaster".

'Nothing to eat or drink'

On the ground, fighting raged in Khan Yunis, Gaza's main southern city, which the Israeli army said it had "encircled".

Palestinian girls carry food supplied by aid agencies.

OCHA said in a bulletin that Israeli forces on Tuesday had issued evacuation orders for a four-square-kilometre (1.5-square-mile) segment of Khan Yunis currently home to around 513,000 people as well as the major Nasser and Al-Amal hospitals.

The office of Palestinian president Mahmud Abbas decried the "dangerous demands" for residents to head south, and warned that Israel intended to "displace the Palestinian people from their homeland, thus leading to unforeseeable consequences", according to official news agency Wafa.