Tens of thousands of fleeing Palestinians sought shelter on Friday as Israeli tanks pushed through the central Gaza Strip, with nearly 200 people reported killed in the past 24 hours of air strikes and artillery barrages on the shattered enclave.

Israeli warplanes attacking the south of Gaza flattened homes and buried families as they slept, residents said.

The new assaults in central and southern Gaza propelled a new exodus of people already driven from other areas in what Israeli Defence Minister Yoav Gallant called an essential stage of its mission to destroy its foe Hamas.

Twelve weeks after Hamas militants stormed Israeli towns, killing 1,200 people and seizing 240 hostages, Israeli forces have laid much of the Gaza Strip to waste.

Nearly all its 2.3 million people have fled their homes at least once and many are now on the move again, often reduced to taking shelter in makeshift tents or huddled under tarpaulins and plastic sheets on open ground.

Gaza health authorities said 187 more Palestinians were confirmed killed in Israeli strikes in the past 24 hours, raising the toll to 21,507 - about 1% of Gaza's population. Thousands more bodies are feared to be buried in the ruins of obliterated neighbourhoods.

In Rafa in the south, journalists at the scene of one air strike that destroyed a building saw the head of a buried toddler sticking out of the rubble.

The child screamed as a rescue worker shielded his head with a hand, while another swung a sledgehammer at a chisel, trying to break up a slab of concrete to free him.

Neighbour Sanad Abu Tabet said the two-storey house had been crowded with displaced people. After morning broke, relatives came to collect the dead wrapped up in white shrouds. A man peeled away the cloth to stroke the face of a dead child.

Tens of thousands of Gazans are fleeing the crowded central districts of Bureij, Maghazi and Nusseirat, ordered out by Israeli forces whose tanks advanced from the north and east.

Most have made their way south or west to the already overwhelmed city of Deir al-Balah.

"We suffered a lot. We had the whole night without shelter, under rain and it was cold, we were with our kids and elderly women," said Um Hamdi, a woman cooking porridge over an open woodfire surrounded by children.

Nearby, Abdel Nasser Awadallah stood inside a wooden frame set up to be wrapped in plastic to make a tent, and spoke of the family he had lost.

"I buried my children - a child 16 years old, another one aged 18. Something I really can't believe, I buried my children at 6 am while their bodies were still warm. Also my nephew, he was 2 years old, I buried him. I buried my wife," he said.

"I never thought in my life that I will bury my children, I thought they would bury me."

Even fleeing did not guarantee safety. Medics and residents said an Israeli air strike also killed two Palestinians in Al-Maghazi refugee camp in central Gaza.

NO SIGN OF SCALING DOWN ISRAELI ASSAULT

Israel says it is doing what it can to avoid civilian casualties, but the high death toll has caused concern even amongst its staunchest allies.

The US has called for it to scale down the full-blown war in coming weeks and move to targeted operations against Hamas leaders. So far Israel shows no sign of doing so, mounting a new assault in the final week of the year with intense bombing of central areas.

Residents say Israeli forces have fought their way deep into Bureij in the battle in central Gaza in the past two days, with intense fighting still taking place on the eastern outskirts. Bombing has been particularly intense there and in adjacent Nusseirat and Maghazi.

Footage filmed by a Palestinian Red Crescent volunteer in Maghazi showed dead and wounded being carried from ruined buildings. Palestinian media reported strikes in Nusseirat had killed at least 35 people overnight.

In the south, Israeli forces have been pounding Khan Younis in preparation for an anticipated further advance into the main southern city, swathes of which they captured in early December.

Defence Minister Gallant said troops were reaching Hamas command centres and arms depots.

"Our operations are essential to achieving the goals of the war. We see the results and the destruction of enemy forces," he said.

Gaza is almost entirely reliant on food, fuel and medical supplies from the outside, and Israel has shut off all access apart from at the southern edge.

International bodies say supplies being let in through Israeli inspections are a small fraction of the enclave's vast needs.

Last week Israel bowed to international pressure to open a second crossing it said would double the number of supply trucks daily to 200, but just 76 were able to enter on Thursday, according to the United Nations, compared to 500 in peacetime.

An Israeli government spokesman said on Friday it does not limit humanitarian aid and the problem was with its distribution inside Gaza.

The United Nations Relief and Works Agency (UNRWA), which distributes aid, rejected allegations it was responsible for hold-ups in deliveries and said the operation was riddled with logistical hurdles.

Bombardments and ground fighting had hampered distribution as well as hold-ups at Israeli checkpoints, it said. A breakdown of law and order also made it hard to secure the convoys, while people were helping themselves to supplies at warehouses.

Israel says it will fight on until it annihilates Hamas, which has sworn to destroy Israel. Palestinians say wiping out the militant group is unachievable because of its diffuse structure and deep roots in a territory it has ruled since 2007.

Efforts by mediators Egypt and Qatar to negotiate a ceasefire have been fruitless since a week-long truce collapsed at the end of November.

Egypt, which hosted the leaders of Hamas and smaller militant group Islamic Jihad in the past week, said on Thursday it was awaiting responses from the warring sides to a proposed peace plan.