At least 112 Palestinians are said to have been killed and 760 injured trying to get desperately needed aid in Gaza.
Crowds descended on a convoy of lorries on the coastal road south-west of Gaza City, in the presence of Israeli tanks.
Israel's military say tanks fired warning shots but did not strike the convoy. Some Palestinians say troops fired directly at them.
A Palestinian witness told the BBC most of those who died had been run over as lorry drivers tried to move forward.
Israeli aerial footage shows hundreds of people on and around lorries, while graphic videos posted online show bodies loaded on to emptied aid lorries and a donkey cart.
Giving the figures of 112 dead and 760 injured, Gaza's Hamas-run health ministry accused Israel of a "massacre".
The UN Security Council has scheduled a closed-door emergency meeting to discuss the incident.
France said "fire by Israeli soldiers against civilians trying to access food" was "unjustifiable" and US President Joe Biden expressed concern the incident would complicate efforts by mediators to broker a temporary ceasefire in the war between Israel and Hamas.
The medical charity MSF said it was "horrified" and called for an "immediate and sustained ceasefire".
The incident came hours before Gaza's health ministry announced that more than 30,000 people, including 21,000 children and women, had been killed in Gaza since the start of the current conflict on 7 October. Some 7,000 were missing and 70,450 were injured, it said.
The UN is warning of a looming famine in the north of the territory, where an estimated 300,000 people are living with little food or clean water.
The Israeli military launched a large-scale air and ground campaign to destroy Hamas - which is proscribed as a terrorist organisation by Israel, the UK and others - after its gunmen killed about 1,200 people in southern Israel and took 253 hostages.
Thursday's incident took place shortly after 04:45 (02:45 GMT) at the Nabulsi roundabout, on the south-western edge of Gaza City.
A convoy of 30 lorries carrying Egyptian aid was making its way north along what the Israel Defense Forces (IDF) described as a "humanitarian corridor" when it was surrounded by civilians, with people climbing on to the trucks.
"Some began violently pushing and even trampling other Gazans to death, looting the humanitarian supplies," said the IDF's chief spokesman, Rear Adm Daniel Hagari. "The unfortunate incident resulted in dozens of Gazans killed and injured."
Israeli tanks, he said, "cautiously tried to disperse the mob with a few warning shots" but pulled back "when the hundreds became thousands and things got out of hand".
"No IDF strike was conducted towards the aid convoy," he said, insisting the Israeli military had been trying to help the aid convoy reach its destination.
Another IDF spokesman said some civilians had approached Israeli soldiers at a nearby checkpoint, ignoring warning shots. Fearing a threat, the soldiers fired at them in a "limited response", he said.
A Palestinian witness, speaking to the BBC, described panic in the crowd and among the drivers, who tried to move forward. Most of those who died were run over, the witness added.
Hamas rejected the IDF's account, citing "undeniable" evidence of "direct firing at citizens, including headshots aimed at immediate killing".
Dozens of casualties in a critical or severe condition were brought to the nearby al-Shifa Hospital in Gaza City, where medics were unable to cope with the sheer volume and severity of cases.
One man at the hospital who was cradling the body of this dead friend, Tamer Shinbari, told the BBC he had gone to the Nabulsi roundabout hoping to get a bag of flour for his family. He said Israeli soldiers had opened fire "and the aid lorry ran over the bodies".
All or most of the casualties being treated at two other hospitals, Kamal Adwan and al-Awda, were said by officials there to have bullet or shrapnel wounds.
Palestinian Authority President Mahmoud Abbas, a rival of Hamas based in the occupied West Bank, accused Israeli forces of a "heinous massacre".
A spokesman for UN Secretary General António Guterres said he condemned the incident and called again for an "immediate humanitarian ceasefire and the unconditional release of all hostages".
The north of Gaza suffered widespread devastation after being the focus of the first phase of the Israeli ground offensive and has been largely cut off from humanitarian assistance for several months.
Last week, the World Food Programme said it had been forced to suspend aid deliveries to the area after its first convoy in three weeks had been surrounded by crowds of hungry people close to an Israeli checkpoint and had then faced gunfire in Gaza City.
On Tuesday, a senior UN aid official warned that at least 576,000 people across the Gaza Strip - one quarter of the population - faced catastrophic levels of food insecurity and one in six children under the age of two in the north were suffering from acute malnutrition and wasting.
Ten children died from dehydration and malnutrition at hospitals in northern Gaza in recent days, the health ministry said.