- "Without a fundamental change, the people of Gaza will face an unprecedented avalanche of human suffering," Mr Guterres said.
- The Palestinian Red Crescent Society said only essential life-saving machines in hospitals, such as incubators for premature babies, were still working.
Hamas gunmen launched an unprecedented attack on Israel from the Gaza Strip on 7 October, killing more than 1,400 people and taking almost 230 hostages.
Since the attack Israel has been carrying out strikes in Gaza. The Hamas-run Palestinian health ministry says the retaliatory strikes have killed more than 7,000 people.
On Friday, Israel said it was intensifying its campaign in Gaza ahead of an expected ground invasion.
What has the Israeli military announced?
An Israeli military spokesman said on Friday night that it was "operating powerfully on all dimensions in order achieve the goals of the war". The air force was conducting extensive strikes on Hamas targets and ground forces were "expanding their operations", he added.
Hamas's military wing, the Izzedine al-Qassam Brigades, said it was fighting Israeli troops in the north-eastern town of Beit Hanoun and the central Bureij area, and that it had fired barrages of rockets towards Israel. It declared that it was ready to confront the "aggression with full force".
Throughout the night, huge explosions lit up the sky above Gaza. At the same time, Palestinian mobile phone and internet networks went down, cutting off communications both inside the Strip and with the outside world. The blackout made it difficult for ambulances to reach the injured.
On Saturday morning, the BBC's Rushdi Abu Alouf, who is in the southern city of Khan Younis, described a scene of "total chaos" on the ground.
He said the bombardment of northern areas was on a scale he had never seen before. There were fewer strikes in southern areas, he added, but there was panic among the hundreds of thousands of people sheltering there after being told by Israel to leave their homes in the north.
The Israeli military has massed tens of thousands of soldiers along the territory's perimeter fence, along with tanks and artillery. It has activated some 300,000 reservists, alongside its standing force of 160,000.
Hamas is thought to have about 25,000 people in its military wing. It also has a vast labyrinth of underground tunnels across Gaza, which it has previously claimed stretch 500km (310 miles).
What is the humanitarian situation in Gaza?
UN Secretary General António Guterres warned on Friday that the humanitarian system in Gaza was "facing a total collapse with unimaginable consequences for more than two million civilians".
He appealed for a humanitarian ceasefire, the unconditional release of all hostages, and the delivery of life-saving supplies of aid at the scale needed.
"Without a fundamental change, the people of Gaza will face an unprecedented avalanche of human suffering," Mr Guterres said.
The World Health Organization said on Tuesday that a third of hospitals in Gaza were no longer functioning due to shortages of electricity, medicine and staff. Those still open were only admitting emergency cases, it added.
The Palestinian Red Crescent Society said only essential life-saving machines in hospitals, such as incubators for premature babies, were still working.
The UN's agency for Palestinian refugees, Unrwa, said on Thursday that it had significantly reduced its humanitarian operations because it had almost exhausted its fuel reserves. More than 600,000 of the 1.4 million people displaced by the fighting have taken refuge inside its facilities.
About 500 lorries per day were crossing into Gaza before the war began. But in recent days, an average of only 12 lorries carrying food, water and medical supplies have entered per day.
The head of the UN's World Food Programme (WFP) says "insane bureaucracy", with extremely stringent checks on lorry cargoes, is slowing the flow of aid through Rafah.
There have also been no shipments of fuel, which is needed to generate electricity for hospitals, shelters, bakeries, water treatment and pumping stations, and the sewerage system.
Israel refuses to allow deliveries of fuel because it says it could be used for military purposes by Hamas. It also says that Hamas is hoarding hundreds of thousands of litres of fuel that it is refusing to hand over to aid agencies.
The southern city of Khan Younis, normally home to 400,000 people, has seen its population increase to about 1.2 million since the Israeli military ordered people leaving in northern areas to evacuate for their own safety. Many families are sharing homes, or sleeping in tents.
However, Israel has continued to carry out strikes on what it says are Hamas military targets in Khan Younis and elsewhere in southern Gaza.
The UN's regional humanitarian chief has said: "Nowhere is safe in Gaza."
What is Hamas and what does it want?
Hamas is a Palestinian group which has ruled the Gaza Strip since 2007. The group is sworn to Israel's destruction and wants to replace it with an Islamic state.
Hamas has fought several wars with Israel since it took power. It has fired - or allowed other groups to fire - thousands of rockets into Israel, and has carried out other deadly attacks.
In response, Israel has repeatedly attacked Hamas with air strikes. In 2008 and 2014, it also sent troops into Gaza.
Together with Egypt, Israel has blockaded the Gaza Strip since 2007 for what it describes as security reasons.
Hamas - or in some cases its military wing, the Izzedine al-Qassam Brigades - has been designated a terrorist group by Israel, the United States, the European Union and the UK, as well as other powers.
Iran backs the group, providing it with funding, weapons and training.
Why is this happening now?
On 7 October, hundreds of Hamas gunmen crossed from the Gaza Strip into southern Israel by breaking through the heavily fortified perimeter fence, landing by sea, and using paragliders.
It was the most serious cross-border attack Israel has faced in more than a generation.
The gunmen killed 1,400 people, most of them civilians, in a series of raids on military posts, kibbutzim and a music festival, and took hostages back into Gaza.
Mr Netanyahu said after the attack that Israel was at war, and vowed that Hamas would "pay an unprecedented price".
Given the resources of Israel's security services, it was astounding that the attack by Hamas was not anticipated, the BBC's security correspondent Frank Gardner says.
It came at a time of soaring Israeli-Palestinian tensions.
This year has been the deadliest on record for Palestinians who live in the Israeli-occupied West Bank, which could have motivated Hamas to strike Israel.
Hamas might also have been seeking to score a significant propaganda victory to boost its popularity among ordinary Palestinians.
The capture of Israeli hostages is thought to be designed to pressure Israel to free some of the estimated 4,500 Palestinians held in Israeli prisons.
The Israeli military says 229 people are still being held in Gaza.
They include 20 children and at least 10 people aged over 60. Soldiers were also taken hostage.
Hamas has so far returned four hostages, with the Gulf state of Qatar acting as a mediator for their release.